0.001/0.001 NO 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty:S v_NonEmpty:S:S M:S:S N:S:S V1:S:S V2:S:S X:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U21 1) 0.001/0.001 (U31 1) 0.001/0.001 (U41 1) 0.001/0.001 (and 1) 0.001/0.001 (isNat 1) 0.001/0.001 (plus 2) 0.001/0.001 (x 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 U11(tt,N:S:S) -> N:S:S 0.001/0.001 U21(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U31(tt) -> num0 0.001/0.001 U41(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> and(isNat(V1:S:S),isNat(V2:S:S)) 0.001/0.001 isNat(x(V1:S:S,V2:S:S)) -> and(isNat(V1:S:S),isNat(V2:S:S)) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> isNat(V1:S:S) 0.001/0.001 plus(N:S:S,num0) -> U11(isNat(N:S:S),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U21(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> U31(isNat(N:S:S)) 0.001/0.001 x(N:S:S,s(M:S:S)) -> U41(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S) 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 CleanTRS Processor: 0.001/0.001 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty:S v_NonEmpty:S:S M:S:S N:S:S V1:S:S V2:S:S X:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U21 1) 0.001/0.001 (U31 1) 0.001/0.001 (U41 1) 0.001/0.001 (and 1) 0.001/0.001 (isNat 1) 0.001/0.001 (plus 2) 0.001/0.001 (x 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 U11(tt,N:S:S) -> N:S:S 0.001/0.001 U21(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U31(tt) -> num0 0.001/0.001 U41(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> and(isNat(V1:S:S),isNat(V2:S:S)) 0.001/0.001 isNat(x(V1:S:S,V2:S:S)) -> and(isNat(V1:S:S),isNat(V2:S:S)) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> isNat(V1:S:S) 0.001/0.001 plus(N:S:S,num0) -> U11(isNat(N:S:S),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U21(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> U31(isNat(N:S:S)) 0.001/0.001 x(N:S:S,s(M:S:S)) -> U41(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S) 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 0.001/0.001 Modular Confluence Combinations Decomposition Processor: 0.001/0.001 It is a CTRS -> No modular confluence 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 CS-TRS Processor: 0.001/0.001 R is a CS-TRS 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 Confluence Problem: 0.001/0.001 (VAR vNonEmpty:S v_NonEmpty:S:S M:S:S N:S:S V1:S:S V2:S:S X:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (U11 1) 0.001/0.001 (U21 1) 0.001/0.001 (U31 1) 0.001/0.001 (U41 1) 0.001/0.001 (and 1) 0.001/0.001 (isNat 1) 0.001/0.001 (plus 2) 0.001/0.001 (x 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (num0) 0.001/0.001 (s) 0.001/0.001 (tt) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 U11(tt,N:S:S) -> N:S:S 0.001/0.001 U21(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U31(tt) -> num0 0.001/0.001 U41(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> and(isNat(V1:S:S),isNat(V2:S:S)) 0.001/0.001 isNat(x(V1:S:S,V2:S:S)) -> and(isNat(V1:S:S),isNat(V2:S:S)) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> isNat(V1:S:S) 0.001/0.001 plus(N:S:S,num0) -> U11(isNat(N:S:S),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U21(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> U31(isNat(N:S:S)) 0.001/0.001 x(N:S:S,s(M:S:S)) -> U41(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S) 0.001/0.001 ) 0.001/0.001 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.001/0.001 0.001/0.001 Huet Levy Processor: 0.001/0.001 -> Rules: 0.001/0.001 U11(tt,N:S:S) -> N:S:S 0.001/0.001 U21(tt,M:S:S,N:S:S) -> s(plus(N:S:S,M:S:S)) 0.001/0.001 U31(tt) -> num0 0.001/0.001 U41(tt,M:S:S,N:S:S) -> plus(x(N:S:S,M:S:S),N:S:S) 0.001/0.001 and(tt,X:S:S) -> X:S:S 0.001/0.001 isNat(plus(V1:S:S,V2:S:S)) -> and(isNat(V1:S:S),isNat(V2:S:S)) 0.001/0.001 isNat(x(V1:S:S,V2:S:S)) -> and(isNat(V1:S:S),isNat(V2:S:S)) 0.001/0.001 isNat(num0) -> tt 0.001/0.001 isNat(s(V1:S:S)) -> isNat(V1:S:S) 0.001/0.001 plus(N:S:S,num0) -> U11(isNat(N:S:S),N:S:S) 0.001/0.001 plus(N:S:S,s(M:S:S)) -> U21(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S) 0.001/0.001 x(N:S:S,num0) -> U31(isNat(N:S:S)) 0.001/0.001 x(N:S:S,s(M:S:S)) -> U41(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S) 0.001/0.001 -> Vars: 0.001/0.001 N:S, M:S, N:S, M:S, N:S, X:S, V1:S, V2:S, V1:S, V2:S, V1:S, N:S, M:S, N:S, N:S, M:S, N:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [V2:S], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V2:S]) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [V2:S], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: [V2:S]) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [V1:S], UV-LFrozen: [V1:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: [N:S]) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [M:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [N:S], UV-LFrozen: [N:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [M:S], UV-LFrozen: [M:S, N:S], UV-RFrozen: [M:S, N:S]) 0.001/0.001 -> FVars: 0.001/0.001 x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23 0.001/0.001 -> PVars: 0.001/0.001 N:S: [x7, x9, x11, x18, x20, x21, x23], M:S: [x8, x10, x19, x22], X:S: [x12], V1:S: [x13, x15, x17], V2:S: [x14, x16] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: U11(tt,x7:S) -> x7:S, id: 1, possubterms: U11(tt,x7:S)->[], tt->[1]) 0.001/0.001 (rule: U21(tt,x8:S,x9:S) -> s(plus(x9:S,x8:S)), id: 2, possubterms: U21(tt,x8:S,x9:S)->[], tt->[1]) 0.001/0.001 (rule: U31(tt) -> num0, id: 3, possubterms: U31(tt)->[], tt->[1]) 0.001/0.001 (rule: U41(tt,x10:S,x11:S) -> plus(x(x11:S,x10:S),x11:S), id: 4, possubterms: U41(tt,x10:S,x11:S)->[], tt->[1]) 0.001/0.001 (rule: and(tt,x12:S) -> x12:S, id: 5, possubterms: and(tt,x12:S)->[], tt->[1]) 0.001/0.001 (rule: isNat(plus(x13:S,x14:S)) -> and(isNat(x13:S),isNat(x14:S)), id: 6, possubterms: isNat(plus(x13:S,x14:S))->[], plus(x13:S,x14:S)->[1]) 0.001/0.001 (rule: isNat(x(x15:S,x16:S)) -> and(isNat(x15:S),isNat(x16:S)), id: 7, possubterms: isNat(x(x15:S,x16:S))->[], x(x15:S,x16:S)->[1]) 0.001/0.001 (rule: isNat(num0) -> tt, id: 8, possubterms: isNat(num0)->[], num0->[1]) 0.001/0.001 (rule: isNat(s(x17:S)) -> isNat(x17:S), id: 9, possubterms: isNat(s(x17:S))->[], s(x17:S)->[1]) 0.001/0.001 (rule: plus(x18:S,num0) -> U11(isNat(x18:S),x18:S), id: 10, possubterms: plus(x18:S,num0)->[], num0->[2]) 0.001/0.001 (rule: plus(x20:S,s(x19:S)) -> U21(and(isNat(x19:S),isNat(x20:S)),x19:S,x20:S), id: 11, possubterms: plus(x20:S,s(x19:S))->[], s(x19:S)->[2]) 0.001/0.001 (rule: x(x21:S,num0) -> U31(isNat(x21:S)), id: 12, possubterms: x(x21:S,num0)->[], num0->[2]) 0.001/0.001 (rule: x(x23:S,s(x22:S)) -> U41(and(isNat(x22:S),isNat(x23:S)),x22:S,x23:S), id: 13, possubterms: x(x23:S,s(x22:S))->[], s(x22:S)->[2]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 (R6 unifies with R10 at p: [1], l: isNat(plus(x13:S,x14:S)), lp: plus(x13:S,x14:S), sig: {x13:S -> N:S:S,x14:S -> num0}, l': plus(N:S:S,num0), r: and(isNat(x13:S),isNat(x14:S)), r': U11(isNat(N:S:S),N:S:S)) 0.001/0.001 (R6 unifies with R11 at p: [1], l: isNat(plus(x13:S,x14:S)), lp: plus(x13:S,x14:S), sig: {x13:S -> N:S:S,x14:S -> s(M:S:S)}, l': plus(N:S:S,s(M:S:S)), r: and(isNat(x13:S),isNat(x14:S)), r': U21(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S)) 0.001/0.001 (R7 unifies with R12 at p: [1], l: isNat(x(x15:S,x16:S)), lp: x(x15:S,x16:S), sig: {x15:S -> N:S:S,x16:S -> num0}, l': x(N:S:S,num0), r: and(isNat(x15:S),isNat(x16:S)), r': U31(isNat(N:S:S))) 0.001/0.001 (R7 unifies with R13 at p: [1], l: isNat(x(x15:S,x16:S)), lp: x(x15:S,x16:S), sig: {x15:S -> N:S:S,x16:S -> s(M:S:S)}, l': x(N:S:S,s(M:S:S)), r: and(isNat(x15:S),isNat(x16:S)), r': U41(and(isNat(M:S:S),isNat(N:S:S)),M:S:S,N:S:S)) 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 => Not trivial, Not overlay, NW0, N1 0.001/0.001 => Not trivial, Not overlay, NW0, N2 0.001/0.001 => Not trivial, Not overlay, NW0, N3 0.001/0.001 => Not trivial, Not overlay, NW0, N4 0.001/0.001 0.001/0.001 -> Problem conclusions: 0.001/0.001 Left linear, Not right linear, Not linear 0.001/0.001 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.001/0.001 Not Huet-Levy confluent, Not Newman confluent 0.001/0.001 R is a CS-TRS, Not left-homogeneous u-replacing variables 0.001/0.001 0.001/0.001 0.001/0.001 Problem 1: 0.001/0.001 Different Normal CP Terms Processor: 0.001/0.001 => Not trivial, Not overlay, NW0, N1, Normal and not trivial cp 0.001/0.001 0.001/0.001 The problem is not joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 66%CPU (0avgtext+0avgdata 10096maxresident)k 0.001/0.001 8inputs+0outputs (0major+796minor)pagefaults 0swaps