0.002/0.002 NO 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S N:S:S X:S:S XS:S:S Y:S:S YS:S:S ZS:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U63 1) 0.002/0.002 (U64 1) 0.002/0.002 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (U82 1) 0.002/0.002 (afterNth) 0.002/0.002 (fst 1) 0.002/0.002 (head 1) 0.002/0.002 (natsFrom) 0.002/0.002 (sel) 0.002/0.002 (snd 1) 0.002/0.002 (splitAt 1 2) 0.002/0.002 (tail 1) 0.002/0.002 (take) 0.002/0.002 (cons) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (num0) 0.002/0.002 (pair) 0.002/0.002 (s) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt,N:S:S,XS:S:S) -> U12(tt,N:S:S,XS:S:S) 0.002/0.002 U12(tt,N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.002/0.002 U21(tt,X:S:S) -> U22(tt,X:S:S) 0.002/0.002 U22(tt,X:S:S) -> X:S:S 0.002/0.002 U31(tt,N:S:S) -> U32(tt,N:S:S) 0.002/0.002 U32(tt,N:S:S) -> N:S:S 0.002/0.002 U41(tt,N:S:S,XS:S:S) -> U42(tt,N:S:S,XS:S:S) 0.002/0.002 U42(tt,N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.002/0.002 U51(tt,Y:S:S) -> U52(tt,Y:S:S) 0.002/0.002 U52(tt,Y:S:S) -> Y:S:S 0.002/0.002 U61(tt,N:S:S,X:S:S,XS:S:S) -> U62(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U62(tt,N:S:S,X:S:S,XS:S:S) -> U63(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U63(tt,N:S:S,X:S:S,XS:S:S) -> U64(splitAt(N:S:S,XS:S:S),X:S:S) 0.002/0.002 U64(pair(YS:S:S,ZS:S:S),X:S:S) -> pair(cons(X:S:S,YS:S:S),ZS:S:S) 0.002/0.002 U71(tt,XS:S:S) -> U72(tt,XS:S:S) 0.002/0.002 U72(tt,XS:S:S) -> XS:S:S 0.002/0.002 U81(tt,N:S:S,XS:S:S) -> U82(tt,N:S:S,XS:S:S) 0.002/0.002 U82(tt,N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.002/0.002 afterNth(N:S:S,XS:S:S) -> U11(tt,N:S:S,XS:S:S) 0.002/0.002 fst(pair(X:S:S,Y:S:S)) -> U21(tt,X:S:S) 0.002/0.002 head(cons(N:S:S,XS:S:S)) -> U31(tt,N:S:S) 0.002/0.002 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.002/0.002 sel(N:S:S,XS:S:S) -> U41(tt,N:S:S,XS:S:S) 0.002/0.002 snd(pair(X:S:S,Y:S:S)) -> U51(tt,Y:S:S) 0.002/0.002 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.002/0.002 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> U61(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 tail(cons(N:S:S,XS:S:S)) -> U71(tt,XS:S:S) 0.002/0.002 take(N:S:S,XS:S:S) -> U81(tt,N:S:S,XS:S:S) 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 CleanTRS Processor: 0.002/0.002 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S N:S:S X:S:S XS:S:S Y:S:S YS:S:S ZS:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U63 1) 0.002/0.002 (U64 1) 0.002/0.002 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (U82 1) 0.002/0.002 (afterNth) 0.002/0.002 (fst 1) 0.002/0.002 (head 1) 0.002/0.002 (natsFrom) 0.002/0.002 (sel) 0.002/0.002 (snd 1) 0.002/0.002 (splitAt 1 2) 0.002/0.002 (tail 1) 0.002/0.002 (take) 0.002/0.002 (cons) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (num0) 0.002/0.002 (pair) 0.002/0.002 (s) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt,N:S:S,XS:S:S) -> U12(tt,N:S:S,XS:S:S) 0.002/0.002 U12(tt,N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.002/0.002 U21(tt,X:S:S) -> U22(tt,X:S:S) 0.002/0.002 U22(tt,X:S:S) -> X:S:S 0.002/0.002 U31(tt,N:S:S) -> U32(tt,N:S:S) 0.002/0.002 U32(tt,N:S:S) -> N:S:S 0.002/0.002 U41(tt,N:S:S,XS:S:S) -> U42(tt,N:S:S,XS:S:S) 0.002/0.002 U42(tt,N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.002/0.002 U51(tt,Y:S:S) -> U52(tt,Y:S:S) 0.002/0.002 U52(tt,Y:S:S) -> Y:S:S 0.002/0.002 U61(tt,N:S:S,X:S:S,XS:S:S) -> U62(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U62(tt,N:S:S,X:S:S,XS:S:S) -> U63(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U63(tt,N:S:S,X:S:S,XS:S:S) -> U64(splitAt(N:S:S,XS:S:S),X:S:S) 0.002/0.002 U64(pair(YS:S:S,ZS:S:S),X:S:S) -> pair(cons(X:S:S,YS:S:S),ZS:S:S) 0.002/0.002 U71(tt,XS:S:S) -> U72(tt,XS:S:S) 0.002/0.002 U72(tt,XS:S:S) -> XS:S:S 0.002/0.002 U81(tt,N:S:S,XS:S:S) -> U82(tt,N:S:S,XS:S:S) 0.002/0.002 U82(tt,N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.002/0.002 afterNth(N:S:S,XS:S:S) -> U11(tt,N:S:S,XS:S:S) 0.002/0.002 fst(pair(X:S:S,Y:S:S)) -> U21(tt,X:S:S) 0.002/0.002 head(cons(N:S:S,XS:S:S)) -> U31(tt,N:S:S) 0.002/0.002 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.002/0.002 sel(N:S:S,XS:S:S) -> U41(tt,N:S:S,XS:S:S) 0.002/0.002 snd(pair(X:S:S,Y:S:S)) -> U51(tt,Y:S:S) 0.002/0.002 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.002/0.002 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> U61(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 tail(cons(N:S:S,XS:S:S)) -> U71(tt,XS:S:S) 0.002/0.002 take(N:S:S,XS:S:S) -> U81(tt,N:S:S,XS:S:S) 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 0.002/0.002 Modular Confluence Combinations Decomposition Processor: 0.002/0.002 It is a CTRS -> No modular confluence 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 CS-TRS Processor: 0.002/0.002 R is a CS-TRS 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S N:S:S X:S:S XS:S:S Y:S:S YS:S:S ZS:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U63 1) 0.002/0.002 (U64 1) 0.002/0.002 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (U82 1) 0.002/0.002 (afterNth) 0.002/0.002 (fst 1) 0.002/0.002 (head 1) 0.002/0.002 (natsFrom) 0.002/0.002 (sel) 0.002/0.002 (snd 1) 0.002/0.002 (splitAt 1 2) 0.002/0.002 (tail 1) 0.002/0.002 (take) 0.002/0.002 (cons) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (num0) 0.002/0.002 (pair) 0.002/0.002 (s) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt,N:S:S,XS:S:S) -> U12(tt,N:S:S,XS:S:S) 0.002/0.002 U12(tt,N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.002/0.002 U21(tt,X:S:S) -> U22(tt,X:S:S) 0.002/0.002 U22(tt,X:S:S) -> X:S:S 0.002/0.002 U31(tt,N:S:S) -> U32(tt,N:S:S) 0.002/0.002 U32(tt,N:S:S) -> N:S:S 0.002/0.002 U41(tt,N:S:S,XS:S:S) -> U42(tt,N:S:S,XS:S:S) 0.002/0.002 U42(tt,N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.002/0.002 U51(tt,Y:S:S) -> U52(tt,Y:S:S) 0.002/0.002 U52(tt,Y:S:S) -> Y:S:S 0.002/0.002 U61(tt,N:S:S,X:S:S,XS:S:S) -> U62(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U62(tt,N:S:S,X:S:S,XS:S:S) -> U63(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U63(tt,N:S:S,X:S:S,XS:S:S) -> U64(splitAt(N:S:S,XS:S:S),X:S:S) 0.002/0.002 U64(pair(YS:S:S,ZS:S:S),X:S:S) -> pair(cons(X:S:S,YS:S:S),ZS:S:S) 0.002/0.002 U71(tt,XS:S:S) -> U72(tt,XS:S:S) 0.002/0.002 U72(tt,XS:S:S) -> XS:S:S 0.002/0.002 U81(tt,N:S:S,XS:S:S) -> U82(tt,N:S:S,XS:S:S) 0.002/0.002 U82(tt,N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.002/0.002 afterNth(N:S:S,XS:S:S) -> U11(tt,N:S:S,XS:S:S) 0.002/0.002 fst(pair(X:S:S,Y:S:S)) -> U21(tt,X:S:S) 0.002/0.002 head(cons(N:S:S,XS:S:S)) -> U31(tt,N:S:S) 0.002/0.002 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.002/0.002 sel(N:S:S,XS:S:S) -> U41(tt,N:S:S,XS:S:S) 0.002/0.002 snd(pair(X:S:S,Y:S:S)) -> U51(tt,Y:S:S) 0.002/0.002 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.002/0.002 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> U61(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 tail(cons(N:S:S,XS:S:S)) -> U71(tt,XS:S:S) 0.002/0.002 take(N:S:S,XS:S:S) -> U81(tt,N:S:S,XS:S:S) 0.002/0.002 ) 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 Extended u-Critical Pairs NonLHRV Processor [JLAMP21]: 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => splitAt(num0,x51:S) -> pair(nil,x51:S) 0.002/0.002 Rule 25 (l' :-> r') => splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.002/0.002 Var => x51:S 0.002/0.002 Pos x51:S in l => [2] 0.002/0.002 Sigma => {x51:S -> splitAt(num0,XS:S:S)} 0.002/0.002 s => pair(nil,splitAt(num0,XS:S:S)) 0.002/0.002 t => splitAt(num0,pair(nil,XS:S:S)) 0.002/0.002 NW => 1 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => splitAt(num0,x51:S) -> pair(nil,x51:S) 0.002/0.002 Rule 26 (l' :-> r') => splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> U61(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 Var => x51:S 0.002/0.002 Pos x51:S in l => [2] 0.002/0.002 Sigma => {x51:S -> splitAt(s(N:S:S),cons(X:S:S,XS:S:S))} 0.002/0.002 s => pair(nil,splitAt(s(N:S:S),cons(X:S:S,XS:S:S))) 0.002/0.002 t => splitAt(num0,U61(tt,N:S:S,X:S:S,XS:S:S)) 0.002/0.002 NW => 1 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => splitAt(num0,x51:S) -> pair(nil,x51:S) 0.002/0.002 Rule 27 (l' :-> r') => tail(cons(N:S:S,XS:S:S)) -> U71(tt,XS:S:S) 0.002/0.002 Var => x51:S 0.002/0.002 Pos x51:S in l => [2] 0.002/0.002 Sigma => {x51:S -> tail(cons(N:S:S,XS:S:S))} 0.002/0.002 s => pair(nil,tail(cons(N:S:S,XS:S:S))) 0.002/0.002 t => splitAt(num0,U71(tt,XS:S:S)) 0.002/0.002 NW => 1 0.002/0.002 0.002/0.002 0.002/0.002 ->Extended u-Critical Pair: 0.002/0.002 Rule 1 (l :-> r) => splitAt(num0,x51:S) -> pair(nil,x51:S) 0.002/0.002 Rule 28 (l' :-> r') => take(N:S:S,XS:S:S) -> U81(tt,N:S:S,XS:S:S) 0.002/0.002 Var => x51:S 0.002/0.002 Pos x51:S in l => [2] 0.002/0.002 Sigma => {x51:S -> take(N:S:S,XS:S:S)} 0.002/0.002 s => pair(nil,take(N:S:S,XS:S:S)) 0.002/0.002 t => splitAt(num0,U81(tt,N:S:S,XS:S:S)) 0.002/0.002 NW => 1 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 Confluence Problem: 0.002/0.002 (VAR vNonEmpty:S v_NonEmpty:S:S N:S:S X:S:S XS:S:S Y:S:S YS:S:S ZS:S:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U12 1) 0.002/0.002 (U21 1) 0.002/0.002 (U22 1) 0.002/0.002 (U31 1) 0.002/0.002 (U32 1) 0.002/0.002 (U41 1) 0.002/0.002 (U42 1) 0.002/0.002 (U51 1) 0.002/0.002 (U52 1) 0.002/0.002 (U61 1) 0.002/0.002 (U62 1) 0.002/0.002 (U63 1) 0.002/0.002 (U64 1) 0.002/0.002 (U71 1) 0.002/0.002 (U72 1) 0.002/0.002 (U81 1) 0.002/0.002 (U82 1) 0.002/0.002 (afterNth) 0.002/0.002 (fst 1) 0.002/0.002 (head 1) 0.002/0.002 (natsFrom) 0.002/0.002 (sel) 0.002/0.002 (snd 1) 0.002/0.002 (splitAt 1 2) 0.002/0.002 (tail 1) 0.002/0.002 (take) 0.002/0.002 (cons) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (nil) 0.002/0.002 (num0) 0.002/0.002 (pair) 0.002/0.002 (s) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt,N:S:S,XS:S:S) -> U12(tt,N:S:S,XS:S:S) 0.002/0.002 U12(tt,N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.002/0.002 U21(tt,X:S:S) -> U22(tt,X:S:S) 0.002/0.002 U22(tt,X:S:S) -> X:S:S 0.002/0.002 U31(tt,N:S:S) -> U32(tt,N:S:S) 0.002/0.002 U32(tt,N:S:S) -> N:S:S 0.002/0.002 U41(tt,N:S:S,XS:S:S) -> U42(tt,N:S:S,XS:S:S) 0.002/0.002 U42(tt,N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.002/0.002 U51(tt,Y:S:S) -> U52(tt,Y:S:S) 0.002/0.002 U52(tt,Y:S:S) -> Y:S:S 0.002/0.002 U61(tt,N:S:S,X:S:S,XS:S:S) -> U62(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U62(tt,N:S:S,X:S:S,XS:S:S) -> U63(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U63(tt,N:S:S,X:S:S,XS:S:S) -> U64(splitAt(N:S:S,XS:S:S),X:S:S) 0.002/0.002 U64(pair(YS:S:S,ZS:S:S),X:S:S) -> pair(cons(X:S:S,YS:S:S),ZS:S:S) 0.002/0.002 U71(tt,XS:S:S) -> U72(tt,XS:S:S) 0.002/0.002 U72(tt,XS:S:S) -> XS:S:S 0.002/0.002 U81(tt,N:S:S,XS:S:S) -> U82(tt,N:S:S,XS:S:S) 0.002/0.002 U82(tt,N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.002/0.002 afterNth(N:S:S,XS:S:S) -> U11(tt,N:S:S,XS:S:S) 0.002/0.002 fst(pair(X:S:S,Y:S:S)) -> U21(tt,X:S:S) 0.002/0.002 head(cons(N:S:S,XS:S:S)) -> U31(tt,N:S:S) 0.002/0.002 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.002/0.002 sel(N:S:S,XS:S:S) -> U41(tt,N:S:S,XS:S:S) 0.002/0.002 snd(pair(X:S:S,Y:S:S)) -> U51(tt,Y:S:S) 0.002/0.002 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.002/0.002 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> U61(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 tail(cons(N:S:S,XS:S:S)) -> U71(tt,XS:S:S) 0.002/0.002 take(N:S:S,XS:S:S) -> U81(tt,N:S:S,XS:S:S) 0.002/0.002 ) 0.002/0.002 Critical Pairs: 0.002/0.002 => Not trivial, Not overlay, NW1, N1 0.002/0.002 => Not trivial, Not overlay, NW1, N2 0.002/0.002 => Not trivial, Not overlay, NW1, N3 0.002/0.002 => Not trivial, Not overlay, NW1, N4 0.002/0.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.002/0.002 0.002/0.002 Huet Levy Processor: 0.002/0.002 -> Rules: 0.002/0.002 U11(tt,N:S:S,XS:S:S) -> U12(tt,N:S:S,XS:S:S) 0.002/0.002 U12(tt,N:S:S,XS:S:S) -> snd(splitAt(N:S:S,XS:S:S)) 0.002/0.002 U21(tt,X:S:S) -> U22(tt,X:S:S) 0.002/0.002 U22(tt,X:S:S) -> X:S:S 0.002/0.002 U31(tt,N:S:S) -> U32(tt,N:S:S) 0.002/0.002 U32(tt,N:S:S) -> N:S:S 0.002/0.002 U41(tt,N:S:S,XS:S:S) -> U42(tt,N:S:S,XS:S:S) 0.002/0.002 U42(tt,N:S:S,XS:S:S) -> head(afterNth(N:S:S,XS:S:S)) 0.002/0.002 U51(tt,Y:S:S) -> U52(tt,Y:S:S) 0.002/0.002 U52(tt,Y:S:S) -> Y:S:S 0.002/0.002 U61(tt,N:S:S,X:S:S,XS:S:S) -> U62(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U62(tt,N:S:S,X:S:S,XS:S:S) -> U63(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 U63(tt,N:S:S,X:S:S,XS:S:S) -> U64(splitAt(N:S:S,XS:S:S),X:S:S) 0.002/0.002 U64(pair(YS:S:S,ZS:S:S),X:S:S) -> pair(cons(X:S:S,YS:S:S),ZS:S:S) 0.002/0.002 U71(tt,XS:S:S) -> U72(tt,XS:S:S) 0.002/0.002 U72(tt,XS:S:S) -> XS:S:S 0.002/0.002 U81(tt,N:S:S,XS:S:S) -> U82(tt,N:S:S,XS:S:S) 0.002/0.002 U82(tt,N:S:S,XS:S:S) -> fst(splitAt(N:S:S,XS:S:S)) 0.002/0.002 afterNth(N:S:S,XS:S:S) -> U11(tt,N:S:S,XS:S:S) 0.002/0.002 fst(pair(X:S:S,Y:S:S)) -> U21(tt,X:S:S) 0.002/0.002 head(cons(N:S:S,XS:S:S)) -> U31(tt,N:S:S) 0.002/0.002 natsFrom(N:S:S) -> cons(N:S:S,natsFrom(s(N:S:S))) 0.002/0.002 sel(N:S:S,XS:S:S) -> U41(tt,N:S:S,XS:S:S) 0.002/0.002 snd(pair(X:S:S,Y:S:S)) -> U51(tt,Y:S:S) 0.002/0.002 splitAt(num0,XS:S:S) -> pair(nil,XS:S:S) 0.002/0.002 splitAt(s(N:S:S),cons(X:S:S,XS:S:S)) -> U61(tt,N:S:S,X:S:S,XS:S:S) 0.002/0.002 tail(cons(N:S:S,XS:S:S)) -> U71(tt,XS:S:S) 0.002/0.002 take(N:S:S,XS:S:S) -> U81(tt,N:S:S,XS:S:S) 0.002/0.002 -> Vars: 0.002/0.002 N:S, XS:S, N:S, XS:S, X:S, X:S, N:S, N:S, N:S, XS:S, N:S, XS:S, Y:S, Y:S, N:S, X:S, XS:S, N:S, X:S, XS:S, N:S, X:S, XS:S, X:S, YS:S, ZS:S, XS:S, XS:S, N:S, XS:S, N:S, XS:S, N:S, XS:S, X:S, Y:S, N:S, XS:S, N:S, N:S, XS:S, X:S, Y:S, XS:S, N:S, X:S, XS:S, N:S, XS:S, N:S, XS:S 0.002/0.002 -> UVars: 0.002/0.002 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [N:S, XS:S]) 0.002/0.002 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [N:S, XS:S], UV-LFrozen: [N:S, XS:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: [X:S]) 0.002/0.002 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S], UV-RFrozen: [N:S]) 0.002/0.002 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [N:S, XS:S]) 0.002/0.002 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [N:S, XS:S]) 0.002/0.002 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y:S], UV-RFrozen: [Y:S]) 0.002/0.002 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [Y:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, X:S, XS:S], UV-RFrozen: [N:S, X:S, XS:S]) 0.002/0.002 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, X:S, XS:S], UV-RFrozen: [N:S, X:S, XS:S]) 0.002/0.002 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [N:S, XS:S], UV-LFrozen: [N:S, X:S, XS:S], UV-RFrozen: [X:S]) 0.002/0.002 (UV-RuleId: 14, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, YS:S, ZS:S], UV-RFrozen: [X:S, YS:S, ZS:S]) 0.002/0.002 (UV-RuleId: 15, UV-LActive: [], UV-RActive: [], UV-LFrozen: [XS:S], UV-RFrozen: [XS:S]) 0.002/0.002 (UV-RuleId: 16, UV-LActive: [], UV-RActive: [XS:S], UV-LFrozen: [XS:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 17, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [N:S, XS:S]) 0.002/0.002 (UV-RuleId: 18, UV-LActive: [], UV-RActive: [N:S, XS:S], UV-LFrozen: [N:S, XS:S], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 19, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [N:S, XS:S]) 0.002/0.002 (UV-RuleId: 20, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S]) 0.002/0.002 (UV-RuleId: 21, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [N:S]) 0.002/0.002 (UV-RuleId: 22, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S], UV-RFrozen: [N:S]) 0.002/0.002 (UV-RuleId: 23, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [N:S, XS:S]) 0.002/0.002 (UV-RuleId: 24, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [Y:S]) 0.002/0.002 (UV-RuleId: 25, UV-LActive: [XS:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [XS:S]) 0.002/0.002 (UV-RuleId: 26, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, X:S, XS:S], UV-RFrozen: [N:S, X:S, XS:S]) 0.002/0.002 (UV-RuleId: 27, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [XS:S]) 0.002/0.002 (UV-RuleId: 28, UV-LActive: [], UV-RActive: [], UV-LFrozen: [N:S, XS:S], UV-RFrozen: [N:S, XS:S]) 0.002/0.002 -> FVars: 0.002/0.002 x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49, x50, x51, x52, x53, x54, x55, x56, x57, x58 0.002/0.002 -> PVars: 0.002/0.002 N:S: [x8, x10, x14, x15, x16, x18, x22, x25, x28, x36, x38, x40, x44, x46, x47, x52, x55, x57], XS:S: [x9, x11, x17, x19, x24, x27, x30, x34, x35, x37, x39, x41, x45, x48, x51, x54, x56, x58], X:S: [x12, x13, x23, x26, x29, x31, x42, x49, x53], Y:S: [x20, x21, x43, x50], YS:S: [x32], ZS:S: [x33] 0.002/0.002 0.002/0.002 -> Rlps: 0.002/0.002 (rule: U11(tt,x8:S,x9:S) -> U12(tt,x8:S,x9:S), id: 1, possubterms: U11(tt,x8:S,x9:S)->[], tt->[1]) 0.002/0.002 (rule: U12(tt,x10:S,x11:S) -> snd(splitAt(x10:S,x11:S)), id: 2, possubterms: U12(tt,x10:S,x11:S)->[], tt->[1]) 0.002/0.002 (rule: U21(tt,x12:S) -> U22(tt,x12:S), id: 3, possubterms: U21(tt,x12:S)->[], tt->[1]) 0.002/0.002 (rule: U22(tt,x13:S) -> x13:S, id: 4, possubterms: U22(tt,x13:S)->[], tt->[1]) 0.002/0.002 (rule: U31(tt,x14:S) -> U32(tt,x14:S), id: 5, possubterms: U31(tt,x14:S)->[], tt->[1]) 0.002/0.002 (rule: U32(tt,x15:S) -> x15:S, id: 6, possubterms: U32(tt,x15:S)->[], tt->[1]) 0.002/0.002 (rule: U41(tt,x16:S,x17:S) -> U42(tt,x16:S,x17:S), id: 7, possubterms: U41(tt,x16:S,x17:S)->[], tt->[1]) 0.002/0.002 (rule: U42(tt,x18:S,x19:S) -> head(afterNth(x18:S,x19:S)), id: 8, possubterms: U42(tt,x18:S,x19:S)->[], tt->[1]) 0.002/0.002 (rule: U51(tt,x20:S) -> U52(tt,x20:S), id: 9, possubterms: U51(tt,x20:S)->[], tt->[1]) 0.002/0.002 (rule: U52(tt,x21:S) -> x21:S, id: 10, possubterms: U52(tt,x21:S)->[], tt->[1]) 0.002/0.002 (rule: U61(tt,x22:S,x23:S,x24:S) -> U62(tt,x22:S,x23:S,x24:S), id: 11, possubterms: U61(tt,x22:S,x23:S,x24:S)->[], tt->[1]) 0.002/0.002 (rule: U62(tt,x25:S,x26:S,x27:S) -> U63(tt,x25:S,x26:S,x27:S), id: 12, possubterms: U62(tt,x25:S,x26:S,x27:S)->[], tt->[1]) 0.002/0.002 (rule: U63(tt,x28:S,x29:S,x30:S) -> U64(splitAt(x28:S,x30:S),x29:S), id: 13, possubterms: U63(tt,x28:S,x29:S,x30:S)->[], tt->[1]) 0.002/0.002 (rule: U64(pair(x32:S,x33:S),x31:S) -> pair(cons(x31:S,x32:S),x33:S), id: 14, possubterms: U64(pair(x32:S,x33:S),x31:S)->[], pair(x32:S,x33:S)->[1]) 0.002/0.002 (rule: U71(tt,x34:S) -> U72(tt,x34:S), id: 15, possubterms: U71(tt,x34:S)->[], tt->[1]) 0.002/0.002 (rule: U72(tt,x35:S) -> x35:S, id: 16, possubterms: U72(tt,x35:S)->[], tt->[1]) 0.002/0.002 (rule: U81(tt,x36:S,x37:S) -> U82(tt,x36:S,x37:S), id: 17, possubterms: U81(tt,x36:S,x37:S)->[], tt->[1]) 0.002/0.002 (rule: U82(tt,x38:S,x39:S) -> fst(splitAt(x38:S,x39:S)), id: 18, possubterms: U82(tt,x38:S,x39:S)->[], tt->[1]) 0.002/0.002 (rule: afterNth(x40:S,x41:S) -> U11(tt,x40:S,x41:S), id: 19, possubterms: afterNth(x40:S,x41:S)->[]) 0.002/0.002 (rule: fst(pair(x42:S,x43:S)) -> U21(tt,x42:S), id: 20, possubterms: fst(pair(x42:S,x43:S))->[], pair(x42:S,x43:S)->[1]) 0.002/0.002 (rule: head(cons(x44:S,x45:S)) -> U31(tt,x44:S), id: 21, possubterms: head(cons(x44:S,x45:S))->[], cons(x44:S,x45:S)->[1]) 0.002/0.002 (rule: natsFrom(x46:S) -> cons(x46:S,natsFrom(s(x46:S))), id: 22, possubterms: natsFrom(x46:S)->[]) 0.002/0.002 (rule: sel(x47:S,x48:S) -> U41(tt,x47:S,x48:S), id: 23, possubterms: sel(x47:S,x48:S)->[]) 0.002/0.002 (rule: snd(pair(x49:S,x50:S)) -> U51(tt,x50:S), id: 24, possubterms: snd(pair(x49:S,x50:S))->[], pair(x49:S,x50:S)->[1]) 0.002/0.002 (rule: splitAt(num0,x51:S) -> pair(nil,x51:S), id: 25, possubterms: splitAt(num0,x51:S)->[], num0->[1]) 0.002/0.002 (rule: splitAt(s(x52:S),cons(x53:S,x54:S)) -> U61(tt,x52:S,x53:S,x54:S), id: 26, possubterms: splitAt(s(x52:S),cons(x53:S,x54:S))->[], s(x52:S)->[1], cons(x53:S,x54:S)->[2]) 0.002/0.002 (rule: tail(cons(x55:S,x56:S)) -> U71(tt,x56:S), id: 27, possubterms: tail(cons(x55:S,x56:S))->[], cons(x55:S,x56:S)->[1]) 0.002/0.002 (rule: take(x57:S,x58:S) -> U81(tt,x57:S,x58:S), id: 28, possubterms: take(x57:S,x58:S)->[]) 0.002/0.002 0.002/0.002 -> Unifications: 0.002/0.002 0.002/0.002 0.002/0.002 -> Critical pairs info: 0.002/0.002 => Not trivial, Not overlay, NW1, N1 0.002/0.002 => Not trivial, Not overlay, NW1, N2 0.002/0.002 => Not trivial, Not overlay, NW1, N3 0.002/0.002 => Not trivial, Not overlay, NW1, N4 0.002/0.002 0.002/0.002 -> Problem conclusions: 0.002/0.002 Left linear, Not right linear, Not linear 0.002/0.002 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.002/0.002 Not Huet-Levy confluent, Not Newman confluent 0.002/0.002 R is a CS-TRS, Not left-homogeneous u-replacing variables 0.002/0.002 0.002/0.002 0.002/0.002 Problem 1: 0.002/0.002 No Convergence Brute Force Processor: 0.002/0.002 -> Rewritings: 0.002/0.002 s: pair(nil,tail(cons(N:S:S,XS:S:S))) 0.002/0.002 Nodes: [0] 0.002/0.002 Edges: [] 0.002/0.002 ID: 0 => ('pair(nil,tail(cons(N:S:S,XS:S:S)))', D0) 0.002/0.002 t: splitAt(num0,U71(tt,XS:S:S)) 0.002/0.002 Nodes: [0,1,2,3,4,5] 0.002/0.002 Edges: [(0,1),(0,2),(1,3),(1,4),(3,5)] 0.002/0.002 ID: 0 => ('splitAt(num0,U71(tt,XS:S:S))', D0) 0.002/0.002 ID: 1 => ('splitAt(num0,U72(tt,XS:S:S))', D1, R15, P[2], S{x34:S -> XS:S:S}), NR: 'U72(tt,XS:S:S)' 0.002/0.002 ID: 2 => ('pair(nil,U71(tt,XS:S:S))', D1, R25, P[], S{x51:S -> U71(tt,XS:S:S)}), NR: 'pair(nil,U71(tt,XS:S:S))' 0.002/0.002 ID: 3 => ('splitAt(num0,XS:S:S)', D2, R16, P[2], S{x35:S -> XS:S:S}), NR: 'XS:S:S' 0.002/0.002 ID: 4 => ('pair(nil,U72(tt,XS:S:S))', D2, R25, P[], S{x51:S -> U72(tt,XS:S:S)}), NR: 'pair(nil,U72(tt,XS:S:S))' 0.002/0.002 ID: 5 => ('pair(nil,XS:S:S)', D3, R25, P[], S{x51:S -> XS:S:S}), NR: 'pair(nil,XS:S:S)' 0.002/0.002 pair(nil,tail(cons(N:S:S,XS:S:S))) ->* no union *<- splitAt(num0,U71(tt,XS:S:S)) 0.002/0.002 "Not joinable" 0.002/0.002 0.002/0.002 The problem is not joinable. 0.002/0.002 0.01user 0.00system 0:00.02elapsed 68%CPU (0avgtext+0avgdata 11508maxresident)k 0.002/0.002 8inputs+0outputs (0major+1123minor)pagefaults 0swaps