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 M:S N:S V1:S V2:S X:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U31 1) 0.002/0.002 (U41 1) 0.002/0.002 (and 1) 0.002/0.002 (isNat) 0.002/0.002 (plus 1 2) 0.002/0.002 (x 1 2) 0.002/0.002 (0) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (s 1) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt,N:S) -> N:S 0.002/0.002 U21(tt,M:S,N:S) -> s(plus(N:S,M:S)) 0.002/0.002 U31(tt) -> 0 0.002/0.002 U41(tt,M:S,N:S) -> plus(x(N:S,M:S),N:S) 0.002/0.002 and(tt,X:S) -> X:S 0.002/0.002 isNat(plus(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(x(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(0) -> tt 0.002/0.002 isNat(s(V1:S)) -> isNat(V1:S) 0.002/0.002 plus(N:S,0) -> U11(isNat(N:S),N:S) 0.002/0.002 plus(N:S,s(M:S)) -> U21(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 x(N:S,0) -> U31(isNat(N:S)) 0.002/0.002 x(N:S,s(M:S)) -> U41(and(isNat(M:S),isNat(N:S)),M:S,N: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 M:S N:S V1:S V2:S X:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U31 1) 0.002/0.002 (U41 1) 0.002/0.002 (and 1) 0.002/0.002 (isNat) 0.002/0.002 (plus 1 2) 0.002/0.002 (x 1 2) 0.002/0.002 (0) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (s 1) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt,N:S) -> N:S 0.002/0.002 U21(tt,M:S,N:S) -> s(plus(N:S,M:S)) 0.002/0.002 U31(tt) -> 0 0.002/0.002 U41(tt,M:S,N:S) -> plus(x(N:S,M:S),N:S) 0.002/0.002 and(tt,X:S) -> X:S 0.002/0.002 isNat(plus(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(x(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(0) -> tt 0.002/0.002 isNat(s(V1:S)) -> isNat(V1:S) 0.002/0.002 plus(N:S,0) -> U11(isNat(N:S),N:S) 0.002/0.002 plus(N:S,s(M:S)) -> U21(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 x(N:S,0) -> U31(isNat(N:S)) 0.002/0.002 x(N:S,s(M:S)) -> U41(and(isNat(M:S),isNat(N:S)),M:S,N: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 M:S N:S V1:S V2:S X:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U31 1) 0.002/0.002 (U41 1) 0.002/0.002 (and 1) 0.002/0.002 (isNat) 0.002/0.002 (plus 1 2) 0.002/0.002 (x 1 2) 0.002/0.002 (0) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (s 1) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt,N:S) -> N:S 0.002/0.002 U21(tt,M:S,N:S) -> s(plus(N:S,M:S)) 0.002/0.002 U31(tt) -> 0 0.002/0.002 U41(tt,M:S,N:S) -> plus(x(N:S,M:S),N:S) 0.002/0.002 and(tt,X:S) -> X:S 0.002/0.002 isNat(plus(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(x(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(0) -> tt 0.002/0.002 isNat(s(V1:S)) -> isNat(V1:S) 0.002/0.002 plus(N:S,0) -> U11(isNat(N:S),N:S) 0.002/0.002 plus(N:S,s(M:S)) -> U21(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 x(N:S,0) -> U31(isNat(N:S)) 0.002/0.002 x(N:S,s(M:S)) -> U41(and(isNat(M:S),isNat(N:S)),M:S,N: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) => plus(x17:S,0) -> U11(isNat(x17:S),x17:S) 0.002/0.002 Rule 10 (l' :-> r') => plus(N:S,0) -> U11(isNat(N:S),N:S) 0.002/0.002 Var => x17:S 0.002/0.002 Pos x17:S in l => [1] 0.002/0.002 Sigma => {x17:S -> plus(N:S,0)} 0.002/0.002 s => U11(isNat(plus(N:S,0)),plus(N:S,0)) 0.002/0.002 t => plus(U11(isNat(N:S),N:S),0) 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) => plus(x17:S,0) -> U11(isNat(x17:S),x17:S) 0.002/0.002 Rule 11 (l' :-> r') => plus(N:S,s(M:S)) -> U21(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 Var => x17:S 0.002/0.002 Pos x17:S in l => [1] 0.002/0.002 Sigma => {x17:S -> plus(N:S,s(M:S))} 0.002/0.002 s => U11(isNat(plus(N:S,s(M:S))),plus(N:S,s(M:S))) 0.002/0.002 t => plus(U21(and(isNat(M:S),isNat(N:S)),M:S,N:S),0) 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) => plus(x17:S,0) -> U11(isNat(x17:S),x17:S) 0.002/0.002 Rule 12 (l' :-> r') => x(N:S,0) -> U31(isNat(N:S)) 0.002/0.002 Var => x17:S 0.002/0.002 Pos x17:S in l => [1] 0.002/0.002 Sigma => {x17:S -> x(N:S,0)} 0.002/0.002 s => U11(isNat(x(N:S,0)),x(N:S,0)) 0.002/0.002 t => plus(U31(isNat(N:S)),0) 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) => plus(x17:S,0) -> U11(isNat(x17:S),x17:S) 0.002/0.002 Rule 13 (l' :-> r') => x(N:S,s(M:S)) -> U41(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 Var => x17:S 0.002/0.002 Pos x17:S in l => [1] 0.002/0.002 Sigma => {x17:S -> x(N:S,s(M:S))} 0.002/0.002 s => U11(isNat(x(N:S,s(M:S))),x(N:S,s(M:S))) 0.002/0.002 t => plus(U41(and(isNat(M:S),isNat(N:S)),M:S,N:S),0) 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) => plus(x19:S,s(x18:S)) -> U21(and(isNat(x18:S),isNat(x19:S)),x18:S,x19:S) 0.002/0.002 Rule 11 (l' :-> r') => plus(N:S,s(M:S)) -> U21(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 Var => x18:S 0.002/0.002 Pos x18:S in l => [2,1] 0.002/0.002 Sigma => {x18:S -> plus(N:S,s(M:S))} 0.002/0.002 s => U21(and(isNat(plus(N:S,s(M:S))),isNat(x19:S)),plus(N:S,s(M:S)),x19:S) 0.002/0.002 t => plus(x19:S,s(U21(and(isNat(M:S),isNat(N:S)),M:S,N: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) => plus(x19:S,s(x18:S)) -> U21(and(isNat(x18:S),isNat(x19:S)),x18:S,x19:S) 0.002/0.002 Rule 12 (l' :-> r') => x(N:S,0) -> U31(isNat(N:S)) 0.002/0.002 Var => x18:S 0.002/0.002 Pos x18:S in l => [2,1] 0.002/0.002 Sigma => {x18:S -> x(N:S,0)} 0.002/0.002 s => U21(and(isNat(x(N:S,0)),isNat(x19:S)),x(N:S,0),x19:S) 0.002/0.002 t => plus(x19:S,s(U31(isNat(N: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) => plus(x19:S,s(x18:S)) -> U21(and(isNat(x18:S),isNat(x19:S)),x18:S,x19:S) 0.002/0.002 Rule 13 (l' :-> r') => x(N:S,s(M:S)) -> U41(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 Var => x18:S 0.002/0.002 Pos x18:S in l => [2,1] 0.002/0.002 Sigma => {x18:S -> x(N:S,s(M:S))} 0.002/0.002 s => U21(and(isNat(x(N:S,s(M:S))),isNat(x19:S)),x(N:S,s(M:S)),x19:S) 0.002/0.002 t => plus(x19:S,s(U41(and(isNat(M:S),isNat(N:S)),M:S,N: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) => x(x20:S,0) -> U31(isNat(x20:S)) 0.002/0.002 Rule 12 (l' :-> r') => x(N:S,0) -> U31(isNat(N:S)) 0.002/0.002 Var => x20:S 0.002/0.002 Pos x20:S in l => [1] 0.002/0.002 Sigma => {x20:S -> x(N:S,0)} 0.002/0.002 s => U31(isNat(x(N:S,0))) 0.002/0.002 t => x(U31(isNat(N:S)),0) 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) => x(x20:S,0) -> U31(isNat(x20:S)) 0.002/0.002 Rule 13 (l' :-> r') => x(N:S,s(M:S)) -> U41(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 Var => x20:S 0.002/0.002 Pos x20:S in l => [1] 0.002/0.002 Sigma => {x20:S -> x(N:S,s(M:S))} 0.002/0.002 s => U31(isNat(x(N:S,s(M:S)))) 0.002/0.002 t => x(U41(and(isNat(M:S),isNat(N:S)),M:S,N:S),0) 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) => x(x22:S,s(x21:S)) -> U41(and(isNat(x21:S),isNat(x22:S)),x21:S,x22:S) 0.002/0.002 Rule 13 (l' :-> r') => x(N:S,s(M:S)) -> U41(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 Var => x21:S 0.002/0.002 Pos x21:S in l => [2,1] 0.002/0.002 Sigma => {x21:S -> x(N:S,s(M:S))} 0.002/0.002 s => U41(and(isNat(x(N:S,s(M:S))),isNat(x22:S)),x(N:S,s(M:S)),x22:S) 0.002/0.002 t => x(x22:S,s(U41(and(isNat(M:S),isNat(N:S)),M:S,N: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 M:S N:S V1:S V2:S X:S) 0.002/0.002 (STRATEGY CONTEXTSENSITIVE 0.002/0.002 (U11 1) 0.002/0.002 (U21 1) 0.002/0.002 (U31 1) 0.002/0.002 (U41 1) 0.002/0.002 (and 1) 0.002/0.002 (isNat) 0.002/0.002 (plus 1 2) 0.002/0.002 (x 1 2) 0.002/0.002 (0) 0.002/0.002 (fSNonEmpty) 0.002/0.002 (s 1) 0.002/0.002 (tt) 0.002/0.002 ) 0.002/0.002 (RULES 0.002/0.002 U11(tt,N:S) -> N:S 0.002/0.002 U21(tt,M:S,N:S) -> s(plus(N:S,M:S)) 0.002/0.002 U31(tt) -> 0 0.002/0.002 U41(tt,M:S,N:S) -> plus(x(N:S,M:S),N:S) 0.002/0.002 and(tt,X:S) -> X:S 0.002/0.002 isNat(plus(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(x(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(0) -> tt 0.002/0.002 isNat(s(V1:S)) -> isNat(V1:S) 0.002/0.002 plus(N:S,0) -> U11(isNat(N:S),N:S) 0.002/0.002 plus(N:S,s(M:S)) -> U21(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 x(N:S,0) -> U31(isNat(N:S)) 0.002/0.002 x(N:S,s(M:S)) -> U41(and(isNat(M:S),isNat(N:S)),M:S,N: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 => Not trivial, Not overlay, NW1, N5 0.002/0.002 => Not trivial, Not overlay, NW1, N6 0.002/0.002 => Not trivial, Not overlay, NW1, N7 0.002/0.002 => Not trivial, Not overlay, NW1, N8 0.002/0.002 => Not trivial, Not overlay, NW1, N9 0.002/0.002 => Not trivial, Not overlay, NW1, N10 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) -> N:S 0.002/0.002 U21(tt,M:S,N:S) -> s(plus(N:S,M:S)) 0.002/0.002 U31(tt) -> 0 0.002/0.002 U41(tt,M:S,N:S) -> plus(x(N:S,M:S),N:S) 0.002/0.002 and(tt,X:S) -> X:S 0.002/0.002 isNat(plus(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(x(V1:S,V2:S)) -> and(isNat(V1:S),isNat(V2:S)) 0.002/0.002 isNat(0) -> tt 0.002/0.002 isNat(s(V1:S)) -> isNat(V1:S) 0.002/0.002 plus(N:S,0) -> U11(isNat(N:S),N:S) 0.002/0.002 plus(N:S,s(M:S)) -> U21(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 x(N:S,0) -> U31(isNat(N:S)) 0.002/0.002 x(N:S,s(M:S)) -> U41(and(isNat(M:S),isNat(N:S)),M:S,N:S) 0.002/0.002 -> Vars: 0.002/0.002 N, M, N, M, N, X, V1, V2, V1, V2, V1, N, M, N, N, M, N 0.002/0.002 -> UVars: 0.002/0.002 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [N], UV-LFrozen: [N], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [M, N], UV-LFrozen: [M, N], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [M, N], UV-LFrozen: [M, N], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [X], UV-LFrozen: [X], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1, V2], UV-RFrozen: [V1, V2]) 0.002/0.002 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.002/0.002 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [], UV-LFrozen: [V1], UV-RFrozen: [V1]) 0.002/0.002 (UV-RuleId: 10, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N]) 0.002/0.002 (UV-RuleId: 11, UV-LActive: [M, N], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [M, N]) 0.002/0.002 (UV-RuleId: 12, UV-LActive: [N], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [N]) 0.002/0.002 (UV-RuleId: 13, UV-LActive: [M, N], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: [M, N]) 0.002/0.002 -> FVars: 0.002/0.002 x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22 0.002/0.002 -> PVars: 0.002/0.002 N: [x6, x8, x10, x17, x19, x20, x22], M: [x7, x9, x18, x21], X: [x11], V1: [x12, x14, x16], V2: [x13, x15] 0.002/0.002 0.002/0.002 -> Rlps: 0.002/0.002 (rule: U11(tt,x6:S) -> x6:S, id: 1, possubterms: U11(tt,x6:S)->[], tt->[1]) 0.002/0.002 (rule: U21(tt,x7:S,x8:S) -> s(plus(x8:S,x7:S)), id: 2, possubterms: U21(tt,x7:S,x8:S)->[], tt->[1]) 0.002/0.002 (rule: U31(tt) -> 0, id: 3, possubterms: U31(tt)->[], tt->[1]) 0.002/0.002 (rule: U41(tt,x9:S,x10:S) -> plus(x(x10:S,x9:S),x10:S), id: 4, possubterms: U41(tt,x9:S,x10:S)->[], tt->[1]) 0.002/0.002 (rule: and(tt,x11:S) -> x11:S, id: 5, possubterms: and(tt,x11:S)->[], tt->[1]) 0.002/0.002 (rule: isNat(plus(x12:S,x13:S)) -> and(isNat(x12:S),isNat(x13:S)), id: 6, possubterms: isNat(plus(x12:S,x13:S))->[]) 0.002/0.002 (rule: isNat(x(x14:S,x15:S)) -> and(isNat(x14:S),isNat(x15:S)), id: 7, possubterms: isNat(x(x14:S,x15:S))->[]) 0.002/0.002 (rule: isNat(0) -> tt, id: 8, possubterms: isNat(0)->[]) 0.002/0.002 (rule: isNat(s(x16:S)) -> isNat(x16:S), id: 9, possubterms: isNat(s(x16:S))->[]) 0.002/0.002 (rule: plus(x17:S,0) -> U11(isNat(x17:S),x17:S), id: 10, possubterms: plus(x17:S,0)->[], 0->[2]) 0.002/0.002 (rule: plus(x19:S,s(x18:S)) -> U21(and(isNat(x18:S),isNat(x19:S)),x18:S,x19:S), id: 11, possubterms: plus(x19:S,s(x18:S))->[], s(x18:S)->[2]) 0.002/0.002 (rule: x(x20:S,0) -> U31(isNat(x20:S)), id: 12, possubterms: x(x20:S,0)->[], 0->[2]) 0.002/0.002 (rule: x(x22:S,s(x21:S)) -> U41(and(isNat(x21:S),isNat(x22:S)),x21:S,x22:S), id: 13, possubterms: x(x22:S,s(x21:S))->[], s(x21:S)->[2]) 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 => Not trivial, Not overlay, NW1, N5 0.002/0.002 => Not trivial, Not overlay, NW1, N6 0.002/0.002 => Not trivial, Not overlay, NW1, N7 0.002/0.002 => Not trivial, Not overlay, NW1, N8 0.002/0.002 => Not trivial, Not overlay, NW1, N9 0.002/0.002 => Not trivial, Not overlay, NW1, N10 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: U21(and(isNat(x(N:S,0)),isNat(N:S)),x(N:S,0),N:S) 0.002/0.002 Nodes: [0,1] 0.002/0.002 Edges: [(0,1)] 0.002/0.002 ID: 0 => ('U21(and(isNat(x(N:S,0)),isNat(N:S)),x(N:S,0),N:S)', D0) 0.002/0.002 ID: 1 => ('U21(and(and(isNat(N:S),isNat(0)),isNat(N:S)),x(N:S,0),N:S)', D1, R7, P[1, 1], S{x14:S -> N:S, x15:S -> 0}), NR: 'and(isNat(N:S),isNat(0))' 0.002/0.002 t: plus(N:S,s(U31(isNat(N:S)))) 0.002/0.002 Nodes: [0,1] 0.002/0.002 Edges: [(0,1)] 0.002/0.002 ID: 0 => ('plus(N:S,s(U31(isNat(N:S))))', D0) 0.002/0.002 ID: 1 => ('U21(and(isNat(U31(isNat(N:S))),isNat(N:S)),U31(isNat(N:S)),N:S)', D1, R11, P[], S{x18:S -> U31(isNat(N:S)), x19:S -> N:S}), NR: 'U21(and(isNat(U31(isNat(N:S))),isNat(N:S)),U31(isNat(N:S)),N:S)' 0.002/0.002 U21(and(isNat(x(N:S,0)),isNat(N:S)),x(N:S,0),N:S) ->* no union *<- plus(N:S,s(U31(isNat(N: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 56%CPU (0avgtext+0avgdata 11232maxresident)k 0.002/0.002 0inputs+0outputs (0major+1103minor)pagefaults 0swaps