MAYBE 794.98/297.03 MAYBE 794.98/297.03 794.98/297.03 We are left with following problem, upon which TcT provides the 794.98/297.03 certificate MAYBE. 794.98/297.03 794.98/297.03 Strict Trs: 794.98/297.03 { U11(tt(), V2) -> U12(isNat(activate(V2))) 794.98/297.03 , U12(tt()) -> tt() 794.98/297.03 , isNat(n__0()) -> tt() 794.98/297.03 , isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) 794.98/297.03 , isNat(n__s(V1)) -> U21(isNat(activate(V1))) 794.98/297.03 , activate(X) -> X 794.98/297.03 , activate(n__0()) -> 0() 794.98/297.03 , activate(n__plus(X1, X2)) -> plus(X1, X2) 794.98/297.03 , activate(n__s(X)) -> s(X) 794.98/297.03 , U21(tt()) -> tt() 794.98/297.03 , U31(tt(), N) -> activate(N) 794.98/297.03 , U41(tt(), M, N) -> 794.98/297.03 U42(isNat(activate(N)), activate(M), activate(N)) 794.98/297.03 , U42(tt(), M, N) -> s(plus(activate(N), activate(M))) 794.98/297.03 , s(X) -> n__s(X) 794.98/297.03 , plus(X1, X2) -> n__plus(X1, X2) 794.98/297.03 , plus(N, s(M)) -> U41(isNat(M), M, N) 794.98/297.03 , plus(N, 0()) -> U31(isNat(N), N) 794.98/297.03 , 0() -> n__0() } 794.98/297.03 Obligation: 794.98/297.03 runtime complexity 794.98/297.03 Answer: 794.98/297.03 MAYBE 794.98/297.03 794.98/297.03 None of the processors succeeded. 794.98/297.03 794.98/297.03 Details of failed attempt(s): 794.98/297.03 ----------------------------- 794.98/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 794.98/297.03 following reason: 794.98/297.03 794.98/297.03 Computation stopped due to timeout after 297.0 seconds. 794.98/297.03 794.98/297.03 2) 'Best' failed due to the following reason: 794.98/297.03 794.98/297.03 None of the processors succeeded. 794.98/297.03 794.98/297.03 Details of failed attempt(s): 794.98/297.03 ----------------------------- 794.98/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 794.98/297.03 seconds)' failed due to the following reason: 794.98/297.03 794.98/297.03 Computation stopped due to timeout after 148.0 seconds. 794.98/297.03 794.98/297.03 2) 'Best' failed due to the following reason: 794.98/297.03 794.98/297.03 None of the processors succeeded. 794.98/297.03 794.98/297.03 Details of failed attempt(s): 794.98/297.03 ----------------------------- 794.98/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 794.98/297.03 following reason: 794.98/297.03 794.98/297.03 The processor is inapplicable, reason: 794.98/297.03 Processor only applicable for innermost runtime complexity analysis 794.98/297.03 794.98/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 794.98/297.03 to the following reason: 794.98/297.03 794.98/297.03 The processor is inapplicable, reason: 794.98/297.03 Processor only applicable for innermost runtime complexity analysis 794.98/297.03 794.98/297.03 794.98/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 794.98/297.03 failed due to the following reason: 794.98/297.03 794.98/297.03 None of the processors succeeded. 794.98/297.03 794.98/297.03 Details of failed attempt(s): 794.98/297.03 ----------------------------- 794.98/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 794.98/297.03 failed due to the following reason: 794.98/297.03 794.98/297.03 match-boundness of the problem could not be verified. 794.98/297.03 794.98/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 794.98/297.03 failed due to the following reason: 794.98/297.03 794.98/297.03 match-boundness of the problem could not be verified. 794.98/297.03 794.98/297.03 794.98/297.03 794.98/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 794.98/297.03 the following reason: 794.98/297.03 794.98/297.03 We add the following weak dependency pairs: 794.98/297.03 794.98/297.03 Strict DPs: 794.98/297.03 { U11^#(tt(), V2) -> c_1(U12^#(isNat(activate(V2)))) 794.98/297.03 , U12^#(tt()) -> c_2() 794.98/297.03 , isNat^#(n__0()) -> c_3() 794.98/297.03 , isNat^#(n__plus(V1, V2)) -> 794.98/297.03 c_4(U11^#(isNat(activate(V1)), activate(V2))) 794.98/297.03 , isNat^#(n__s(V1)) -> c_5(U21^#(isNat(activate(V1)))) 794.98/297.03 , U21^#(tt()) -> c_10() 794.98/297.03 , activate^#(X) -> c_6(X) 794.98/297.03 , activate^#(n__0()) -> c_7(0^#()) 794.98/297.03 , activate^#(n__plus(X1, X2)) -> c_8(plus^#(X1, X2)) 794.98/297.03 , activate^#(n__s(X)) -> c_9(s^#(X)) 794.98/297.03 , 0^#() -> c_18() 794.98/297.03 , plus^#(X1, X2) -> c_15(X1, X2) 794.98/297.03 , plus^#(N, s(M)) -> c_16(U41^#(isNat(M), M, N)) 794.98/297.03 , plus^#(N, 0()) -> c_17(U31^#(isNat(N), N)) 794.98/297.03 , s^#(X) -> c_14(X) 794.98/297.03 , U31^#(tt(), N) -> c_11(activate^#(N)) 794.98/297.03 , U41^#(tt(), M, N) -> 794.98/297.03 c_12(U42^#(isNat(activate(N)), activate(M), activate(N))) 794.98/297.03 , U42^#(tt(), M, N) -> c_13(s^#(plus(activate(N), activate(M)))) } 794.98/297.03 794.98/297.03 and mark the set of starting terms. 794.98/297.03 794.98/297.03 We are left with following problem, upon which TcT provides the 794.98/297.03 certificate MAYBE. 794.98/297.03 794.98/297.03 Strict DPs: 794.98/297.03 { U11^#(tt(), V2) -> c_1(U12^#(isNat(activate(V2)))) 794.98/297.03 , U12^#(tt()) -> c_2() 794.98/297.03 , isNat^#(n__0()) -> c_3() 794.98/297.03 , isNat^#(n__plus(V1, V2)) -> 794.98/297.03 c_4(U11^#(isNat(activate(V1)), activate(V2))) 794.98/297.03 , isNat^#(n__s(V1)) -> c_5(U21^#(isNat(activate(V1)))) 794.98/297.03 , U21^#(tt()) -> c_10() 794.98/297.03 , activate^#(X) -> c_6(X) 794.98/297.03 , activate^#(n__0()) -> c_7(0^#()) 794.98/297.03 , activate^#(n__plus(X1, X2)) -> c_8(plus^#(X1, X2)) 794.98/297.03 , activate^#(n__s(X)) -> c_9(s^#(X)) 794.98/297.03 , 0^#() -> c_18() 794.98/297.03 , plus^#(X1, X2) -> c_15(X1, X2) 794.98/297.03 , plus^#(N, s(M)) -> c_16(U41^#(isNat(M), M, N)) 794.98/297.03 , plus^#(N, 0()) -> c_17(U31^#(isNat(N), N)) 794.98/297.03 , s^#(X) -> c_14(X) 794.98/297.03 , U31^#(tt(), N) -> c_11(activate^#(N)) 794.98/297.03 , U41^#(tt(), M, N) -> 794.98/297.03 c_12(U42^#(isNat(activate(N)), activate(M), activate(N))) 794.98/297.03 , U42^#(tt(), M, N) -> c_13(s^#(plus(activate(N), activate(M)))) } 794.98/297.03 Strict Trs: 794.98/297.03 { U11(tt(), V2) -> U12(isNat(activate(V2))) 794.98/297.03 , U12(tt()) -> tt() 794.98/297.03 , isNat(n__0()) -> tt() 794.98/297.03 , isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) 794.98/297.03 , isNat(n__s(V1)) -> U21(isNat(activate(V1))) 794.98/297.03 , activate(X) -> X 794.98/297.03 , activate(n__0()) -> 0() 794.98/297.03 , activate(n__plus(X1, X2)) -> plus(X1, X2) 794.98/297.03 , activate(n__s(X)) -> s(X) 794.98/297.03 , U21(tt()) -> tt() 794.98/297.03 , U31(tt(), N) -> activate(N) 794.98/297.03 , U41(tt(), M, N) -> 794.98/297.03 U42(isNat(activate(N)), activate(M), activate(N)) 794.98/297.03 , U42(tt(), M, N) -> s(plus(activate(N), activate(M))) 794.98/297.03 , s(X) -> n__s(X) 794.98/297.03 , plus(X1, X2) -> n__plus(X1, X2) 794.98/297.03 , plus(N, s(M)) -> U41(isNat(M), M, N) 794.98/297.03 , plus(N, 0()) -> U31(isNat(N), N) 794.98/297.03 , 0() -> n__0() } 794.98/297.03 Obligation: 794.98/297.03 runtime complexity 794.98/297.03 Answer: 794.98/297.03 MAYBE 794.98/297.03 794.98/297.03 We estimate the number of application of {2,3,6,11} by applications 794.98/297.03 of Pre({2,3,6,11}) = {1,5,7,8,12,15}. Here rules are labeled as 794.98/297.03 follows: 794.98/297.03 794.98/297.03 DPs: 794.98/297.03 { 1: U11^#(tt(), V2) -> c_1(U12^#(isNat(activate(V2)))) 794.98/297.03 , 2: U12^#(tt()) -> c_2() 794.98/297.03 , 3: isNat^#(n__0()) -> c_3() 794.98/297.03 , 4: isNat^#(n__plus(V1, V2)) -> 794.98/297.03 c_4(U11^#(isNat(activate(V1)), activate(V2))) 794.98/297.03 , 5: isNat^#(n__s(V1)) -> c_5(U21^#(isNat(activate(V1)))) 794.98/297.03 , 6: U21^#(tt()) -> c_10() 794.98/297.03 , 7: activate^#(X) -> c_6(X) 794.98/297.03 , 8: activate^#(n__0()) -> c_7(0^#()) 794.98/297.03 , 9: activate^#(n__plus(X1, X2)) -> c_8(plus^#(X1, X2)) 794.98/297.03 , 10: activate^#(n__s(X)) -> c_9(s^#(X)) 794.98/297.03 , 11: 0^#() -> c_18() 794.98/297.03 , 12: plus^#(X1, X2) -> c_15(X1, X2) 794.98/297.03 , 13: plus^#(N, s(M)) -> c_16(U41^#(isNat(M), M, N)) 794.98/297.03 , 14: plus^#(N, 0()) -> c_17(U31^#(isNat(N), N)) 794.98/297.03 , 15: s^#(X) -> c_14(X) 794.98/297.03 , 16: U31^#(tt(), N) -> c_11(activate^#(N)) 794.98/297.03 , 17: U41^#(tt(), M, N) -> 794.98/297.03 c_12(U42^#(isNat(activate(N)), activate(M), activate(N))) 794.98/297.03 , 18: U42^#(tt(), M, N) -> 794.98/297.03 c_13(s^#(plus(activate(N), activate(M)))) } 794.98/297.03 794.98/297.03 We are left with following problem, upon which TcT provides the 794.98/297.03 certificate MAYBE. 794.98/297.03 794.98/297.03 Strict DPs: 794.98/297.03 { U11^#(tt(), V2) -> c_1(U12^#(isNat(activate(V2)))) 794.98/297.03 , isNat^#(n__plus(V1, V2)) -> 794.98/297.03 c_4(U11^#(isNat(activate(V1)), activate(V2))) 794.98/297.03 , isNat^#(n__s(V1)) -> c_5(U21^#(isNat(activate(V1)))) 794.98/297.03 , activate^#(X) -> c_6(X) 794.98/297.03 , activate^#(n__0()) -> c_7(0^#()) 794.98/297.03 , activate^#(n__plus(X1, X2)) -> c_8(plus^#(X1, X2)) 794.98/297.03 , activate^#(n__s(X)) -> c_9(s^#(X)) 794.98/297.03 , plus^#(X1, X2) -> c_15(X1, X2) 794.98/297.03 , plus^#(N, s(M)) -> c_16(U41^#(isNat(M), M, N)) 794.98/297.03 , plus^#(N, 0()) -> c_17(U31^#(isNat(N), N)) 794.98/297.03 , s^#(X) -> c_14(X) 794.98/297.03 , U31^#(tt(), N) -> c_11(activate^#(N)) 794.98/297.03 , U41^#(tt(), M, N) -> 794.98/297.03 c_12(U42^#(isNat(activate(N)), activate(M), activate(N))) 794.98/297.03 , U42^#(tt(), M, N) -> c_13(s^#(plus(activate(N), activate(M)))) } 794.98/297.03 Strict Trs: 794.98/297.03 { U11(tt(), V2) -> U12(isNat(activate(V2))) 794.98/297.03 , U12(tt()) -> tt() 794.98/297.03 , isNat(n__0()) -> tt() 794.98/297.03 , isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) 794.98/297.03 , isNat(n__s(V1)) -> U21(isNat(activate(V1))) 794.98/297.03 , activate(X) -> X 794.98/297.03 , activate(n__0()) -> 0() 794.98/297.03 , activate(n__plus(X1, X2)) -> plus(X1, X2) 794.98/297.03 , activate(n__s(X)) -> s(X) 794.98/297.03 , U21(tt()) -> tt() 794.98/297.03 , U31(tt(), N) -> activate(N) 794.98/297.03 , U41(tt(), M, N) -> 794.98/297.03 U42(isNat(activate(N)), activate(M), activate(N)) 794.98/297.04 , U42(tt(), M, N) -> s(plus(activate(N), activate(M))) 794.98/297.04 , s(X) -> n__s(X) 794.98/297.04 , plus(X1, X2) -> n__plus(X1, X2) 794.98/297.04 , plus(N, s(M)) -> U41(isNat(M), M, N) 794.98/297.04 , plus(N, 0()) -> U31(isNat(N), N) 794.98/297.04 , 0() -> n__0() } 794.98/297.04 Weak DPs: 794.98/297.04 { U12^#(tt()) -> c_2() 794.98/297.04 , isNat^#(n__0()) -> c_3() 794.98/297.04 , U21^#(tt()) -> c_10() 794.98/297.04 , 0^#() -> c_18() } 794.98/297.04 Obligation: 794.98/297.04 runtime complexity 794.98/297.04 Answer: 794.98/297.04 MAYBE 794.98/297.04 794.98/297.04 We estimate the number of application of {1,3,5} by applications of 794.98/297.04 Pre({1,3,5}) = {2,4,8,11,12}. Here rules are labeled as follows: 794.98/297.04 794.98/297.04 DPs: 794.98/297.04 { 1: U11^#(tt(), V2) -> c_1(U12^#(isNat(activate(V2)))) 794.98/297.04 , 2: isNat^#(n__plus(V1, V2)) -> 794.98/297.04 c_4(U11^#(isNat(activate(V1)), activate(V2))) 794.98/297.04 , 3: isNat^#(n__s(V1)) -> c_5(U21^#(isNat(activate(V1)))) 794.98/297.04 , 4: activate^#(X) -> c_6(X) 794.98/297.04 , 5: activate^#(n__0()) -> c_7(0^#()) 794.98/297.04 , 6: activate^#(n__plus(X1, X2)) -> c_8(plus^#(X1, X2)) 794.98/297.04 , 7: activate^#(n__s(X)) -> c_9(s^#(X)) 794.98/297.04 , 8: plus^#(X1, X2) -> c_15(X1, X2) 794.98/297.04 , 9: plus^#(N, s(M)) -> c_16(U41^#(isNat(M), M, N)) 794.98/297.04 , 10: plus^#(N, 0()) -> c_17(U31^#(isNat(N), N)) 794.98/297.04 , 11: s^#(X) -> c_14(X) 794.98/297.04 , 12: U31^#(tt(), N) -> c_11(activate^#(N)) 794.98/297.04 , 13: U41^#(tt(), M, N) -> 794.98/297.04 c_12(U42^#(isNat(activate(N)), activate(M), activate(N))) 794.98/297.04 , 14: U42^#(tt(), M, N) -> 794.98/297.04 c_13(s^#(plus(activate(N), activate(M)))) 794.98/297.04 , 15: U12^#(tt()) -> c_2() 794.98/297.04 , 16: isNat^#(n__0()) -> c_3() 794.98/297.04 , 17: U21^#(tt()) -> c_10() 794.98/297.04 , 18: 0^#() -> c_18() } 794.98/297.04 794.98/297.04 We are left with following problem, upon which TcT provides the 794.98/297.04 certificate MAYBE. 794.98/297.04 794.98/297.04 Strict DPs: 794.98/297.04 { isNat^#(n__plus(V1, V2)) -> 794.98/297.04 c_4(U11^#(isNat(activate(V1)), activate(V2))) 794.98/297.04 , activate^#(X) -> c_6(X) 794.98/297.04 , activate^#(n__plus(X1, X2)) -> c_8(plus^#(X1, X2)) 794.98/297.04 , activate^#(n__s(X)) -> c_9(s^#(X)) 794.98/297.04 , plus^#(X1, X2) -> c_15(X1, X2) 794.98/297.04 , plus^#(N, s(M)) -> c_16(U41^#(isNat(M), M, N)) 794.98/297.04 , plus^#(N, 0()) -> c_17(U31^#(isNat(N), N)) 794.98/297.04 , s^#(X) -> c_14(X) 794.98/297.04 , U31^#(tt(), N) -> c_11(activate^#(N)) 794.98/297.04 , U41^#(tt(), M, N) -> 794.98/297.04 c_12(U42^#(isNat(activate(N)), activate(M), activate(N))) 794.98/297.04 , U42^#(tt(), M, N) -> c_13(s^#(plus(activate(N), activate(M)))) } 794.98/297.04 Strict Trs: 794.98/297.04 { U11(tt(), V2) -> U12(isNat(activate(V2))) 794.98/297.04 , U12(tt()) -> tt() 794.98/297.04 , isNat(n__0()) -> tt() 794.98/297.04 , isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) 794.98/297.04 , isNat(n__s(V1)) -> U21(isNat(activate(V1))) 794.98/297.04 , activate(X) -> X 794.98/297.04 , activate(n__0()) -> 0() 794.98/297.04 , activate(n__plus(X1, X2)) -> plus(X1, X2) 794.98/297.04 , activate(n__s(X)) -> s(X) 794.98/297.04 , U21(tt()) -> tt() 794.98/297.04 , U31(tt(), N) -> activate(N) 794.98/297.04 , U41(tt(), M, N) -> 794.98/297.04 U42(isNat(activate(N)), activate(M), activate(N)) 794.98/297.04 , U42(tt(), M, N) -> s(plus(activate(N), activate(M))) 794.98/297.04 , s(X) -> n__s(X) 794.98/297.04 , plus(X1, X2) -> n__plus(X1, X2) 794.98/297.04 , plus(N, s(M)) -> U41(isNat(M), M, N) 794.98/297.04 , plus(N, 0()) -> U31(isNat(N), N) 794.98/297.04 , 0() -> n__0() } 794.98/297.04 Weak DPs: 794.98/297.04 { U11^#(tt(), V2) -> c_1(U12^#(isNat(activate(V2)))) 794.98/297.04 , U12^#(tt()) -> c_2() 794.98/297.04 , isNat^#(n__0()) -> c_3() 794.98/297.04 , isNat^#(n__s(V1)) -> c_5(U21^#(isNat(activate(V1)))) 794.98/297.04 , U21^#(tt()) -> c_10() 794.98/297.04 , activate^#(n__0()) -> c_7(0^#()) 794.98/297.04 , 0^#() -> c_18() } 794.98/297.04 Obligation: 794.98/297.04 runtime complexity 794.98/297.04 Answer: 794.98/297.04 MAYBE 794.98/297.04 794.98/297.04 We estimate the number of application of {1} by applications of 794.98/297.04 Pre({1}) = {2,5,8}. Here rules are labeled as follows: 794.98/297.04 794.98/297.04 DPs: 794.98/297.04 { 1: isNat^#(n__plus(V1, V2)) -> 794.98/297.04 c_4(U11^#(isNat(activate(V1)), activate(V2))) 794.98/297.04 , 2: activate^#(X) -> c_6(X) 794.98/297.04 , 3: activate^#(n__plus(X1, X2)) -> c_8(plus^#(X1, X2)) 794.98/297.04 , 4: activate^#(n__s(X)) -> c_9(s^#(X)) 794.98/297.04 , 5: plus^#(X1, X2) -> c_15(X1, X2) 794.98/297.04 , 6: plus^#(N, s(M)) -> c_16(U41^#(isNat(M), M, N)) 794.98/297.04 , 7: plus^#(N, 0()) -> c_17(U31^#(isNat(N), N)) 794.98/297.04 , 8: s^#(X) -> c_14(X) 794.98/297.04 , 9: U31^#(tt(), N) -> c_11(activate^#(N)) 794.98/297.04 , 10: U41^#(tt(), M, N) -> 794.98/297.04 c_12(U42^#(isNat(activate(N)), activate(M), activate(N))) 794.98/297.04 , 11: U42^#(tt(), M, N) -> 794.98/297.04 c_13(s^#(plus(activate(N), activate(M)))) 794.98/297.04 , 12: U11^#(tt(), V2) -> c_1(U12^#(isNat(activate(V2)))) 794.98/297.04 , 13: U12^#(tt()) -> c_2() 794.98/297.04 , 14: isNat^#(n__0()) -> c_3() 794.98/297.04 , 15: isNat^#(n__s(V1)) -> c_5(U21^#(isNat(activate(V1)))) 794.98/297.04 , 16: U21^#(tt()) -> c_10() 794.98/297.04 , 17: activate^#(n__0()) -> c_7(0^#()) 794.98/297.04 , 18: 0^#() -> c_18() } 794.98/297.04 794.98/297.04 We are left with following problem, upon which TcT provides the 794.98/297.04 certificate MAYBE. 794.98/297.04 794.98/297.04 Strict DPs: 794.98/297.04 { activate^#(X) -> c_6(X) 794.98/297.04 , activate^#(n__plus(X1, X2)) -> c_8(plus^#(X1, X2)) 794.98/297.04 , activate^#(n__s(X)) -> c_9(s^#(X)) 794.98/297.04 , plus^#(X1, X2) -> c_15(X1, X2) 794.98/297.04 , plus^#(N, s(M)) -> c_16(U41^#(isNat(M), M, N)) 794.98/297.04 , plus^#(N, 0()) -> c_17(U31^#(isNat(N), N)) 794.98/297.04 , s^#(X) -> c_14(X) 794.98/297.04 , U31^#(tt(), N) -> c_11(activate^#(N)) 794.98/297.04 , U41^#(tt(), M, N) -> 794.98/297.04 c_12(U42^#(isNat(activate(N)), activate(M), activate(N))) 794.98/297.04 , U42^#(tt(), M, N) -> c_13(s^#(plus(activate(N), activate(M)))) } 794.98/297.04 Strict Trs: 794.98/297.04 { U11(tt(), V2) -> U12(isNat(activate(V2))) 794.98/297.04 , U12(tt()) -> tt() 794.98/297.04 , isNat(n__0()) -> tt() 794.98/297.04 , isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2)) 794.98/297.04 , isNat(n__s(V1)) -> U21(isNat(activate(V1))) 794.98/297.04 , activate(X) -> X 794.98/297.04 , activate(n__0()) -> 0() 794.98/297.04 , activate(n__plus(X1, X2)) -> plus(X1, X2) 794.98/297.04 , activate(n__s(X)) -> s(X) 794.98/297.04 , U21(tt()) -> tt() 794.98/297.04 , U31(tt(), N) -> activate(N) 794.98/297.04 , U41(tt(), M, N) -> 794.98/297.04 U42(isNat(activate(N)), activate(M), activate(N)) 794.98/297.04 , U42(tt(), M, N) -> s(plus(activate(N), activate(M))) 794.98/297.04 , s(X) -> n__s(X) 794.98/297.04 , plus(X1, X2) -> n__plus(X1, X2) 794.98/297.04 , plus(N, s(M)) -> U41(isNat(M), M, N) 794.98/297.04 , plus(N, 0()) -> U31(isNat(N), N) 794.98/297.04 , 0() -> n__0() } 794.98/297.04 Weak DPs: 794.98/297.04 { U11^#(tt(), V2) -> c_1(U12^#(isNat(activate(V2)))) 794.98/297.04 , U12^#(tt()) -> c_2() 794.98/297.04 , isNat^#(n__0()) -> c_3() 794.98/297.04 , isNat^#(n__plus(V1, V2)) -> 794.98/297.04 c_4(U11^#(isNat(activate(V1)), activate(V2))) 794.98/297.04 , isNat^#(n__s(V1)) -> c_5(U21^#(isNat(activate(V1)))) 794.98/297.04 , U21^#(tt()) -> c_10() 794.98/297.04 , activate^#(n__0()) -> c_7(0^#()) 794.98/297.04 , 0^#() -> c_18() } 794.98/297.04 Obligation: 794.98/297.04 runtime complexity 794.98/297.04 Answer: 794.98/297.04 MAYBE 794.98/297.04 794.98/297.04 Empty strict component of the problem is NOT empty. 794.98/297.04 794.98/297.04 794.98/297.04 Arrrr.. 795.20/297.28 EOF