0.001/0.001 YES 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 N:S:S X:S:S Y:S:S Z:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (from) 0.001/0.001 (num2ndsneg 1 2) 0.001/0.001 (num2ndspos 1 2) 0.001/0.001 (pi) 0.001/0.001 (plus 1) 0.001/0.001 (square) 0.001/0.001 (times 1) 0.001/0.001 (cons) 0.001/0.001 (cons2 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (negrecip 1) 0.001/0.001 (num0) 0.001/0.001 (posrecip 1) 0.001/0.001 (rcons 1 2) 0.001/0.001 (rnil) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 num2ndsneg(num0,Z:S:S) -> rnil 0.001/0.001 num2ndsneg(s(N:S:S),cons(X:S:S,Z:S:S)) -> num2ndsneg(s(N:S:S),cons2(X:S:S,Z:S:S)) 0.001/0.001 num2ndsneg(s(N:S:S),cons2(X:S:S,cons(Y:S:S,Z:S:S))) -> rcons(negrecip(Y:S:S),num2ndspos(N:S:S,Z:S:S)) 0.001/0.001 num2ndspos(num0,Z:S:S) -> rnil 0.001/0.001 num2ndspos(s(N:S:S),cons(X:S:S,Z:S:S)) -> num2ndspos(s(N:S:S),cons2(X:S:S,Z:S:S)) 0.001/0.001 num2ndspos(s(N:S:S),cons2(X:S:S,cons(Y:S:S,Z:S:S))) -> rcons(posrecip(Y:S:S),num2ndsneg(N:S:S,Z:S:S)) 0.001/0.001 pi(X:S:S) -> num2ndspos(X:S:S,from(num0)) 0.001/0.001 plus(num0,Y:S:S) -> Y:S:S 0.001/0.001 plus(s(X:S:S),Y:S:S) -> s(plus(X:S:S,Y:S:S)) 0.001/0.001 square(X:S:S) -> times(X:S:S,X:S:S) 0.001/0.001 times(num0,Y:S:S) -> num0 0.001/0.001 times(s(X:S:S),Y:S:S) -> plus(Y:S:S,times(X:S:S,Y: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 N:S:S X:S:S Y:S:S Z:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (from) 0.001/0.001 (num2ndsneg 1 2) 0.001/0.001 (num2ndspos 1 2) 0.001/0.001 (pi) 0.001/0.001 (plus 1) 0.001/0.001 (square) 0.001/0.001 (times 1) 0.001/0.001 (cons) 0.001/0.001 (cons2 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (negrecip 1) 0.001/0.001 (num0) 0.001/0.001 (posrecip 1) 0.001/0.001 (rcons 1 2) 0.001/0.001 (rnil) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 num2ndsneg(num0,Z:S:S) -> rnil 0.001/0.001 num2ndsneg(s(N:S:S),cons(X:S:S,Z:S:S)) -> num2ndsneg(s(N:S:S),cons2(X:S:S,Z:S:S)) 0.001/0.001 num2ndsneg(s(N:S:S),cons2(X:S:S,cons(Y:S:S,Z:S:S))) -> rcons(negrecip(Y:S:S),num2ndspos(N:S:S,Z:S:S)) 0.001/0.001 num2ndspos(num0,Z:S:S) -> rnil 0.001/0.001 num2ndspos(s(N:S:S),cons(X:S:S,Z:S:S)) -> num2ndspos(s(N:S:S),cons2(X:S:S,Z:S:S)) 0.001/0.001 num2ndspos(s(N:S:S),cons2(X:S:S,cons(Y:S:S,Z:S:S))) -> rcons(posrecip(Y:S:S),num2ndsneg(N:S:S,Z:S:S)) 0.001/0.001 pi(X:S:S) -> num2ndspos(X:S:S,from(num0)) 0.001/0.001 plus(num0,Y:S:S) -> Y:S:S 0.001/0.001 plus(s(X:S:S),Y:S:S) -> s(plus(X:S:S,Y:S:S)) 0.001/0.001 square(X:S:S) -> times(X:S:S,X:S:S) 0.001/0.001 times(num0,Y:S:S) -> num0 0.001/0.001 times(s(X:S:S),Y:S:S) -> plus(Y:S:S,times(X:S:S,Y: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 Left-Homogeneous u-Replacing Variables Processor: 0.001/0.001 R satisfies LHRV condition 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 N:S:S X:S:S Y:S:S Z:S:S) 0.001/0.001 (STRATEGY CONTEXTSENSITIVE 0.001/0.001 (from) 0.001/0.001 (num2ndsneg 1 2) 0.001/0.001 (num2ndspos 1 2) 0.001/0.001 (pi) 0.001/0.001 (plus 1) 0.001/0.001 (square) 0.001/0.001 (times 1) 0.001/0.001 (cons) 0.001/0.001 (cons2 2) 0.001/0.001 (fSNonEmpty) 0.001/0.001 (negrecip 1) 0.001/0.001 (num0) 0.001/0.001 (posrecip 1) 0.001/0.001 (rcons 1 2) 0.001/0.001 (rnil) 0.001/0.001 (s) 0.001/0.001 ) 0.001/0.001 (RULES 0.001/0.001 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 num2ndsneg(num0,Z:S:S) -> rnil 0.001/0.001 num2ndsneg(s(N:S:S),cons(X:S:S,Z:S:S)) -> num2ndsneg(s(N:S:S),cons2(X:S:S,Z:S:S)) 0.001/0.001 num2ndsneg(s(N:S:S),cons2(X:S:S,cons(Y:S:S,Z:S:S))) -> rcons(negrecip(Y:S:S),num2ndspos(N:S:S,Z:S:S)) 0.001/0.001 num2ndspos(num0,Z:S:S) -> rnil 0.001/0.001 num2ndspos(s(N:S:S),cons(X:S:S,Z:S:S)) -> num2ndspos(s(N:S:S),cons2(X:S:S,Z:S:S)) 0.001/0.001 num2ndspos(s(N:S:S),cons2(X:S:S,cons(Y:S:S,Z:S:S))) -> rcons(posrecip(Y:S:S),num2ndsneg(N:S:S,Z:S:S)) 0.001/0.001 pi(X:S:S) -> num2ndspos(X:S:S,from(num0)) 0.001/0.001 plus(num0,Y:S:S) -> Y:S:S 0.001/0.001 plus(s(X:S:S),Y:S:S) -> s(plus(X:S:S,Y:S:S)) 0.001/0.001 square(X:S:S) -> times(X:S:S,X:S:S) 0.001/0.001 times(num0,Y:S:S) -> num0 0.001/0.001 times(s(X:S:S),Y:S:S) -> plus(Y:S:S,times(X:S:S,Y: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 from(X:S:S) -> cons(X:S:S,from(s(X:S:S))) 0.001/0.001 num2ndsneg(num0,Z:S:S) -> rnil 0.001/0.001 num2ndsneg(s(N:S:S),cons(X:S:S,Z:S:S)) -> num2ndsneg(s(N:S:S),cons2(X:S:S,Z:S:S)) 0.001/0.001 num2ndsneg(s(N:S:S),cons2(X:S:S,cons(Y:S:S,Z:S:S))) -> rcons(negrecip(Y:S:S),num2ndspos(N:S:S,Z:S:S)) 0.001/0.001 num2ndspos(num0,Z:S:S) -> rnil 0.001/0.001 num2ndspos(s(N:S:S),cons(X:S:S,Z:S:S)) -> num2ndspos(s(N:S:S),cons2(X:S:S,Z:S:S)) 0.001/0.001 num2ndspos(s(N:S:S),cons2(X:S:S,cons(Y:S:S,Z:S:S))) -> rcons(posrecip(Y:S:S),num2ndsneg(N:S:S,Z:S:S)) 0.001/0.001 pi(X:S:S) -> num2ndspos(X:S:S,from(num0)) 0.001/0.001 plus(num0,Y:S:S) -> Y:S:S 0.001/0.001 plus(s(X:S:S),Y:S:S) -> s(plus(X:S:S,Y:S:S)) 0.001/0.001 square(X:S:S) -> times(X:S:S,X:S:S) 0.001/0.001 times(num0,Y:S:S) -> num0 0.001/0.001 times(s(X:S:S),Y:S:S) -> plus(Y:S:S,times(X:S:S,Y:S:S)) 0.001/0.001 -> Vars: 0.001/0.001 X:S, Z:S, N:S, X:S, Z:S, N:S, X:S, Y:S, Z:S, Z:S, N:S, X:S, Z:S, N:S, X:S, Y:S, Z:S, X:S, Y:S, X:S, Y:S, X:S, Y:S, X:S, Y:S 0.001/0.001 -> UVars: 0.001/0.001 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S], UV-RFrozen: [X:S]) 0.001/0.001 (UV-RuleId: 2, UV-LActive: [Z:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [Z:S], UV-LFrozen: [N:S, X:S, Z:S], UV-RFrozen: [N:S, X:S]) 0.001/0.001 (UV-RuleId: 4, UV-LActive: [], UV-RActive: [N:S, Y:S, Z:S], UV-LFrozen: [N:S, X:S, Y:S, Z:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 5, UV-LActive: [Z:S], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 6, UV-LActive: [], UV-RActive: [Z:S], UV-LFrozen: [N:S, X:S, Z:S], UV-RFrozen: [N:S, X:S]) 0.001/0.001 (UV-RuleId: 7, UV-LActive: [], UV-RActive: [N:S, Y:S, Z:S], UV-LFrozen: [N:S, X:S, Y:S, Z:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 8, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 9, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 10, UV-LActive: [], UV-RActive: [], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.001/0.001 (UV-RuleId: 11, UV-LActive: [], UV-RActive: [X:S], UV-LFrozen: [X:S], UV-RFrozen: [X:S]) 0.001/0.001 (UV-RuleId: 12, UV-LActive: [], UV-RActive: [], UV-LFrozen: [Y:S], UV-RFrozen: []) 0.001/0.001 (UV-RuleId: 13, UV-LActive: [], UV-RActive: [Y:S], UV-LFrozen: [X:S, Y:S], UV-RFrozen: [X:S, Y:S]) 0.001/0.001 -> FVars: 0.001/0.001 x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30 0.001/0.001 -> PVars: 0.001/0.001 X:S: [x6, x9, x12, x17, x20, x23, x25, x27, x29], Z:S: [x7, x10, x14, x15, x18, x22], N:S: [x8, x11, x16, x19], Y:S: [x13, x21, x24, x26, x28, x30] 0.001/0.001 0.001/0.001 -> Rlps: 0.001/0.001 (rule: from(x6:S) -> cons(x6:S,from(s(x6:S))), id: 1, possubterms: from(x6:S)->[]) 0.001/0.001 (rule: num2ndsneg(num0,x7:S) -> rnil, id: 2, possubterms: num2ndsneg(num0,x7:S)->[], num0->[1]) 0.001/0.001 (rule: num2ndsneg(s(x8:S),cons(x9:S,x10:S)) -> num2ndsneg(s(x8:S),cons2(x9:S,x10:S)), id: 3, possubterms: num2ndsneg(s(x8:S),cons(x9:S,x10:S))->[], s(x8:S)->[1], cons(x9:S,x10:S)->[2]) 0.001/0.001 (rule: num2ndsneg(s(x11:S),cons2(x12:S,cons(x13:S,x14:S))) -> rcons(negrecip(x13:S),num2ndspos(x11:S,x14:S)), id: 4, possubterms: num2ndsneg(s(x11:S),cons2(x12:S,cons(x13:S,x14:S)))->[], s(x11:S)->[1], cons2(x12:S,cons(x13:S,x14:S))->[2], cons(x13:S,x14:S)->[2, 2]) 0.001/0.001 (rule: num2ndspos(num0,x15:S) -> rnil, id: 5, possubterms: num2ndspos(num0,x15:S)->[], num0->[1]) 0.001/0.001 (rule: num2ndspos(s(x16:S),cons(x17:S,x18:S)) -> num2ndspos(s(x16:S),cons2(x17:S,x18:S)), id: 6, possubterms: num2ndspos(s(x16:S),cons(x17:S,x18:S))->[], s(x16:S)->[1], cons(x17:S,x18:S)->[2]) 0.001/0.001 (rule: num2ndspos(s(x19:S),cons2(x20:S,cons(x21:S,x22:S))) -> rcons(posrecip(x21:S),num2ndsneg(x19:S,x22:S)), id: 7, possubterms: num2ndspos(s(x19:S),cons2(x20:S,cons(x21:S,x22:S)))->[], s(x19:S)->[1], cons2(x20:S,cons(x21:S,x22:S))->[2], cons(x21:S,x22:S)->[2, 2]) 0.001/0.001 (rule: pi(x23:S) -> num2ndspos(x23:S,from(num0)), id: 8, possubterms: pi(x23:S)->[]) 0.001/0.001 (rule: plus(num0,x24:S) -> x24:S, id: 9, possubterms: plus(num0,x24:S)->[], num0->[1]) 0.001/0.001 (rule: plus(s(x25:S),x26:S) -> s(plus(x25:S,x26:S)), id: 10, possubterms: plus(s(x25:S),x26:S)->[], s(x25:S)->[1]) 0.001/0.001 (rule: square(x27:S) -> times(x27:S,x27:S), id: 11, possubterms: square(x27:S)->[]) 0.001/0.001 (rule: times(num0,x28:S) -> num0, id: 12, possubterms: times(num0,x28:S)->[], num0->[1]) 0.001/0.001 (rule: times(s(x29:S),x30:S) -> plus(x30:S,times(x29:S,x30:S)), id: 13, possubterms: times(s(x29:S),x30:S)->[], s(x29:S)->[1]) 0.001/0.001 0.001/0.001 -> Unifications: 0.001/0.001 0.001/0.001 0.001/0.001 -> Critical pairs info: 0.001/0.001 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 Weakly orthogonal, Almost orthogonal, Orthogonal 0.001/0.001 Huet-Levy confluent, Not Newman confluent 0.001/0.001 R is a CS-TRS, Left-homogeneous u-replacing variables 0.001/0.001 0.001/0.001 0.001/0.001 The problem is joinable. 0.001/0.001 0.00user 0.00system 0:00.01elapsed 50%CPU (0avgtext+0avgdata 9796maxresident)k 0.001/0.001 8inputs+0outputs (0major+786minor)pagefaults 0swaps