MAYBE 1184.79/297.42 MAYBE 1184.79/297.42 1184.79/297.42 We are left with following problem, upon which TcT provides the 1184.79/297.42 certificate MAYBE. 1184.79/297.42 1184.79/297.42 Strict Trs: 1184.79/297.42 { a__U11(X1, X2) -> U11(X1, X2) 1184.79/297.42 , a__U11(tt(), V2) -> a__U12(a__isNat(V2)) 1184.79/297.42 , a__U12(X) -> U12(X) 1184.79/297.42 , a__U12(tt()) -> tt() 1184.79/297.42 , a__isNat(X) -> isNat(X) 1184.79/297.42 , a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 1184.79/297.42 , a__isNat(0()) -> tt() 1184.79/297.42 , a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) 1184.79/297.42 , a__U21(X) -> U21(X) 1184.79/297.42 , a__U21(tt()) -> tt() 1184.79/297.42 , a__U31(X1, X2) -> U31(X1, X2) 1184.79/297.42 , a__U31(tt(), N) -> mark(N) 1184.79/297.42 , mark(tt()) -> tt() 1184.79/297.42 , mark(s(X)) -> s(mark(X)) 1184.79/297.42 , mark(0()) -> 0() 1184.79/297.42 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1184.79/297.42 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1184.79/297.42 , mark(U12(X)) -> a__U12(mark(X)) 1184.79/297.42 , mark(isNat(X)) -> a__isNat(X) 1184.79/297.42 , mark(U21(X)) -> a__U21(mark(X)) 1184.79/297.42 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1184.79/297.42 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1184.79/297.42 , mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1184.79/297.42 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1184.79/297.42 , a__U41(tt(), M, N) -> a__U42(a__isNat(N), M, N) 1184.79/297.42 , a__U42(X1, X2, X3) -> U42(X1, X2, X3) 1184.79/297.42 , a__U42(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1184.79/297.42 , a__plus(X1, X2) -> plus(X1, X2) 1184.79/297.42 , a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) 1184.79/297.42 , a__plus(N, 0()) -> a__U31(a__isNat(N), N) } 1184.79/297.42 Obligation: 1184.79/297.42 runtime complexity 1184.79/297.42 Answer: 1184.79/297.42 MAYBE 1184.79/297.42 1184.79/297.42 None of the processors succeeded. 1184.79/297.42 1184.79/297.42 Details of failed attempt(s): 1184.79/297.42 ----------------------------- 1184.79/297.42 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1184.79/297.42 following reason: 1184.79/297.42 1184.79/297.42 Computation stopped due to timeout after 297.0 seconds. 1184.79/297.42 1184.79/297.42 2) 'Best' failed due to the following reason: 1184.79/297.42 1184.79/297.42 None of the processors succeeded. 1184.79/297.42 1184.79/297.42 Details of failed attempt(s): 1184.79/297.42 ----------------------------- 1184.79/297.42 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1184.79/297.42 seconds)' failed due to the following reason: 1184.79/297.42 1184.79/297.42 None of the processors succeeded. 1184.79/297.42 1184.79/297.42 Details of failed attempt(s): 1184.79/297.42 ----------------------------- 1184.79/297.42 1) 'empty' failed due to the following reason: 1184.79/297.42 1184.79/297.42 Empty strict component of the problem is NOT empty. 1184.79/297.43 1184.79/297.43 2) 'With Problem ...' failed due to the following reason: 1184.79/297.43 1184.79/297.43 None of the processors succeeded. 1184.79/297.43 1184.79/297.43 Details of failed attempt(s): 1184.79/297.43 ----------------------------- 1184.79/297.43 1) 'empty' failed due to the following reason: 1184.79/297.43 1184.79/297.43 Empty strict component of the problem is NOT empty. 1184.79/297.43 1184.79/297.43 2) 'Fastest' failed due to the following reason: 1184.79/297.43 1184.79/297.43 None of the processors succeeded. 1184.79/297.43 1184.79/297.43 Details of failed attempt(s): 1184.79/297.43 ----------------------------- 1184.79/297.43 1) 'With Problem ...' failed due to the following reason: 1184.79/297.43 1184.79/297.43 None of the processors succeeded. 1184.79/297.43 1184.79/297.43 Details of failed attempt(s): 1184.79/297.43 ----------------------------- 1184.79/297.43 1) 'empty' failed due to the following reason: 1184.79/297.43 1184.79/297.43 Empty strict component of the problem is NOT empty. 1184.79/297.43 1184.79/297.43 2) 'With Problem ...' failed due to the following reason: 1184.79/297.43 1184.79/297.43 None of the processors succeeded. 1184.79/297.43 1184.79/297.43 Details of failed attempt(s): 1184.79/297.43 ----------------------------- 1184.79/297.43 1) 'empty' failed due to the following reason: 1184.79/297.43 1184.79/297.43 Empty strict component of the problem is NOT empty. 1184.79/297.43 1184.79/297.43 2) 'With Problem ...' failed due to the following reason: 1184.79/297.43 1184.79/297.43 None of the processors succeeded. 1184.79/297.43 1184.79/297.43 Details of failed attempt(s): 1184.79/297.43 ----------------------------- 1184.79/297.43 1) 'empty' failed due to the following reason: 1184.79/297.43 1184.79/297.43 Empty strict component of the problem is NOT empty. 1184.79/297.43 1184.79/297.43 2) 'With Problem ...' failed due to the following reason: 1184.79/297.43 1184.79/297.43 Empty strict component of the problem is NOT empty. 1184.79/297.43 1184.79/297.43 1184.79/297.43 1184.79/297.43 1184.79/297.43 2) 'With Problem ...' failed due to the following reason: 1184.79/297.43 1184.79/297.43 None of the processors succeeded. 1184.79/297.43 1184.79/297.43 Details of failed attempt(s): 1184.79/297.43 ----------------------------- 1184.79/297.43 1) 'empty' failed due to the following reason: 1184.79/297.43 1184.79/297.43 Empty strict component of the problem is NOT empty. 1184.79/297.43 1184.79/297.43 2) 'With Problem ...' failed due to the following reason: 1184.79/297.43 1184.79/297.43 Empty strict component of the problem is NOT empty. 1184.79/297.43 1184.79/297.43 1184.79/297.43 1184.79/297.43 1184.79/297.43 1184.79/297.43 2) 'Best' failed due to the following reason: 1184.79/297.43 1184.79/297.43 None of the processors succeeded. 1184.79/297.43 1184.79/297.43 Details of failed attempt(s): 1184.79/297.43 ----------------------------- 1184.79/297.43 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1184.79/297.43 to the following reason: 1184.79/297.43 1184.79/297.43 The processor is inapplicable, reason: 1184.79/297.43 Processor only applicable for innermost runtime complexity analysis 1184.79/297.43 1184.79/297.43 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1184.79/297.43 following reason: 1184.79/297.43 1184.79/297.43 The processor is inapplicable, reason: 1184.79/297.43 Processor only applicable for innermost runtime complexity analysis 1184.79/297.43 1184.79/297.43 1184.79/297.43 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1184.79/297.43 failed due to the following reason: 1184.79/297.43 1184.79/297.43 None of the processors succeeded. 1184.79/297.43 1184.79/297.43 Details of failed attempt(s): 1184.79/297.43 ----------------------------- 1184.79/297.43 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1184.79/297.43 failed due to the following reason: 1184.79/297.43 1184.79/297.43 match-boundness of the problem could not be verified. 1184.79/297.43 1184.79/297.43 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1184.79/297.43 failed due to the following reason: 1184.79/297.43 1184.79/297.43 match-boundness of the problem could not be verified. 1184.79/297.43 1184.79/297.43 1184.79/297.43 1184.79/297.43 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1184.79/297.43 the following reason: 1184.79/297.43 1184.79/297.43 We add the following weak dependency pairs: 1184.79/297.43 1184.79/297.43 Strict DPs: 1184.79/297.43 { a__U11^#(X1, X2) -> c_1(X1, X2) 1184.79/297.43 , a__U11^#(tt(), V2) -> c_2(a__U12^#(a__isNat(V2))) 1184.79/297.43 , a__U12^#(X) -> c_3(X) 1184.79/297.43 , a__U12^#(tt()) -> c_4() 1184.79/297.43 , a__isNat^#(X) -> c_5(X) 1184.79/297.43 , a__isNat^#(s(V1)) -> c_6(a__U21^#(a__isNat(V1))) 1184.79/297.43 , a__isNat^#(0()) -> c_7() 1184.79/297.43 , a__isNat^#(plus(V1, V2)) -> c_8(a__U11^#(a__isNat(V1), V2)) 1184.79/297.43 , a__U21^#(X) -> c_9(X) 1184.79/297.43 , a__U21^#(tt()) -> c_10() 1184.79/297.43 , a__U31^#(X1, X2) -> c_11(X1, X2) 1184.79/297.43 , a__U31^#(tt(), N) -> c_12(mark^#(N)) 1184.79/297.43 , mark^#(tt()) -> c_13() 1184.79/297.43 , mark^#(s(X)) -> c_14(mark^#(X)) 1184.79/297.43 , mark^#(0()) -> c_15() 1184.79/297.43 , mark^#(plus(X1, X2)) -> c_16(a__plus^#(mark(X1), mark(X2))) 1184.79/297.43 , mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2)) 1184.79/297.43 , mark^#(U12(X)) -> c_18(a__U12^#(mark(X))) 1184.79/297.43 , mark^#(isNat(X)) -> c_19(a__isNat^#(X)) 1184.79/297.43 , mark^#(U21(X)) -> c_20(a__U21^#(mark(X))) 1184.79/297.43 , mark^#(U31(X1, X2)) -> c_21(a__U31^#(mark(X1), X2)) 1184.79/297.43 , mark^#(U41(X1, X2, X3)) -> c_22(a__U41^#(mark(X1), X2, X3)) 1184.79/297.43 , mark^#(U42(X1, X2, X3)) -> c_23(a__U42^#(mark(X1), X2, X3)) 1184.79/297.43 , a__plus^#(X1, X2) -> c_28(X1, X2) 1184.79/297.43 , a__plus^#(N, s(M)) -> c_29(a__U41^#(a__isNat(M), M, N)) 1184.79/297.43 , a__plus^#(N, 0()) -> c_30(a__U31^#(a__isNat(N), N)) 1184.79/297.43 , a__U41^#(X1, X2, X3) -> c_24(X1, X2, X3) 1184.79/297.43 , a__U41^#(tt(), M, N) -> c_25(a__U42^#(a__isNat(N), M, N)) 1184.79/297.43 , a__U42^#(X1, X2, X3) -> c_26(X1, X2, X3) 1184.79/297.43 , a__U42^#(tt(), M, N) -> c_27(a__plus^#(mark(N), mark(M))) } 1184.79/297.43 1184.79/297.43 and mark the set of starting terms. 1184.79/297.43 1184.79/297.43 We are left with following problem, upon which TcT provides the 1184.79/297.43 certificate MAYBE. 1184.79/297.43 1184.79/297.43 Strict DPs: 1184.79/297.43 { a__U11^#(X1, X2) -> c_1(X1, X2) 1184.79/297.43 , a__U11^#(tt(), V2) -> c_2(a__U12^#(a__isNat(V2))) 1184.79/297.43 , a__U12^#(X) -> c_3(X) 1184.79/297.43 , a__U12^#(tt()) -> c_4() 1184.79/297.43 , a__isNat^#(X) -> c_5(X) 1184.79/297.43 , a__isNat^#(s(V1)) -> c_6(a__U21^#(a__isNat(V1))) 1184.79/297.44 , a__isNat^#(0()) -> c_7() 1184.79/297.44 , a__isNat^#(plus(V1, V2)) -> c_8(a__U11^#(a__isNat(V1), V2)) 1184.79/297.44 , a__U21^#(X) -> c_9(X) 1184.79/297.44 , a__U21^#(tt()) -> c_10() 1184.79/297.44 , a__U31^#(X1, X2) -> c_11(X1, X2) 1184.79/297.44 , a__U31^#(tt(), N) -> c_12(mark^#(N)) 1184.79/297.44 , mark^#(tt()) -> c_13() 1184.79/297.44 , mark^#(s(X)) -> c_14(mark^#(X)) 1184.79/297.44 , mark^#(0()) -> c_15() 1184.79/297.44 , mark^#(plus(X1, X2)) -> c_16(a__plus^#(mark(X1), mark(X2))) 1184.79/297.44 , mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2)) 1184.79/297.44 , mark^#(U12(X)) -> c_18(a__U12^#(mark(X))) 1184.79/297.44 , mark^#(isNat(X)) -> c_19(a__isNat^#(X)) 1184.79/297.44 , mark^#(U21(X)) -> c_20(a__U21^#(mark(X))) 1184.79/297.44 , mark^#(U31(X1, X2)) -> c_21(a__U31^#(mark(X1), X2)) 1184.79/297.44 , mark^#(U41(X1, X2, X3)) -> c_22(a__U41^#(mark(X1), X2, X3)) 1184.79/297.44 , mark^#(U42(X1, X2, X3)) -> c_23(a__U42^#(mark(X1), X2, X3)) 1184.79/297.44 , a__plus^#(X1, X2) -> c_28(X1, X2) 1184.79/297.44 , a__plus^#(N, s(M)) -> c_29(a__U41^#(a__isNat(M), M, N)) 1184.79/297.44 , a__plus^#(N, 0()) -> c_30(a__U31^#(a__isNat(N), N)) 1184.79/297.44 , a__U41^#(X1, X2, X3) -> c_24(X1, X2, X3) 1184.79/297.44 , a__U41^#(tt(), M, N) -> c_25(a__U42^#(a__isNat(N), M, N)) 1184.79/297.44 , a__U42^#(X1, X2, X3) -> c_26(X1, X2, X3) 1184.79/297.44 , a__U42^#(tt(), M, N) -> c_27(a__plus^#(mark(N), mark(M))) } 1184.79/297.44 Strict Trs: 1184.79/297.44 { a__U11(X1, X2) -> U11(X1, X2) 1184.79/297.44 , a__U11(tt(), V2) -> a__U12(a__isNat(V2)) 1184.79/297.44 , a__U12(X) -> U12(X) 1184.79/297.44 , a__U12(tt()) -> tt() 1184.79/297.44 , a__isNat(X) -> isNat(X) 1184.79/297.44 , a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 1184.79/297.44 , a__isNat(0()) -> tt() 1184.79/297.44 , a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) 1184.79/297.44 , a__U21(X) -> U21(X) 1184.79/297.44 , a__U21(tt()) -> tt() 1184.79/297.44 , a__U31(X1, X2) -> U31(X1, X2) 1184.79/297.44 , a__U31(tt(), N) -> mark(N) 1184.79/297.44 , mark(tt()) -> tt() 1184.79/297.44 , mark(s(X)) -> s(mark(X)) 1184.79/297.44 , mark(0()) -> 0() 1184.79/297.44 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1184.79/297.44 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1184.79/297.44 , mark(U12(X)) -> a__U12(mark(X)) 1184.79/297.44 , mark(isNat(X)) -> a__isNat(X) 1184.79/297.44 , mark(U21(X)) -> a__U21(mark(X)) 1184.79/297.44 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1184.79/297.44 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1184.79/297.44 , mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1184.79/297.44 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1184.79/297.44 , a__U41(tt(), M, N) -> a__U42(a__isNat(N), M, N) 1184.79/297.44 , a__U42(X1, X2, X3) -> U42(X1, X2, X3) 1184.79/297.44 , a__U42(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1184.79/297.44 , a__plus(X1, X2) -> plus(X1, X2) 1184.79/297.44 , a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) 1184.79/297.44 , a__plus(N, 0()) -> a__U31(a__isNat(N), N) } 1184.79/297.44 Obligation: 1184.79/297.44 runtime complexity 1184.79/297.44 Answer: 1184.79/297.44 MAYBE 1184.79/297.44 1184.79/297.44 We estimate the number of application of {4,7,10,13,15} by 1184.79/297.44 applications of Pre({4,7,10,13,15}) = 1184.79/297.44 {1,2,3,5,6,9,11,12,14,18,19,20,24,27,29}. Here rules are labeled as 1184.79/297.44 follows: 1184.79/297.44 1184.79/297.44 DPs: 1184.79/297.44 { 1: a__U11^#(X1, X2) -> c_1(X1, X2) 1184.79/297.44 , 2: a__U11^#(tt(), V2) -> c_2(a__U12^#(a__isNat(V2))) 1184.79/297.44 , 3: a__U12^#(X) -> c_3(X) 1184.79/297.44 , 4: a__U12^#(tt()) -> c_4() 1184.79/297.44 , 5: a__isNat^#(X) -> c_5(X) 1184.79/297.44 , 6: a__isNat^#(s(V1)) -> c_6(a__U21^#(a__isNat(V1))) 1184.79/297.44 , 7: a__isNat^#(0()) -> c_7() 1184.79/297.44 , 8: a__isNat^#(plus(V1, V2)) -> c_8(a__U11^#(a__isNat(V1), V2)) 1184.79/297.44 , 9: a__U21^#(X) -> c_9(X) 1184.79/297.44 , 10: a__U21^#(tt()) -> c_10() 1184.79/297.44 , 11: a__U31^#(X1, X2) -> c_11(X1, X2) 1184.79/297.44 , 12: a__U31^#(tt(), N) -> c_12(mark^#(N)) 1184.79/297.44 , 13: mark^#(tt()) -> c_13() 1184.79/297.44 , 14: mark^#(s(X)) -> c_14(mark^#(X)) 1184.79/297.44 , 15: mark^#(0()) -> c_15() 1184.79/297.44 , 16: mark^#(plus(X1, X2)) -> c_16(a__plus^#(mark(X1), mark(X2))) 1184.79/297.44 , 17: mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2)) 1184.79/297.44 , 18: mark^#(U12(X)) -> c_18(a__U12^#(mark(X))) 1184.79/297.44 , 19: mark^#(isNat(X)) -> c_19(a__isNat^#(X)) 1184.79/297.44 , 20: mark^#(U21(X)) -> c_20(a__U21^#(mark(X))) 1184.79/297.44 , 21: mark^#(U31(X1, X2)) -> c_21(a__U31^#(mark(X1), X2)) 1184.79/297.44 , 22: mark^#(U41(X1, X2, X3)) -> c_22(a__U41^#(mark(X1), X2, X3)) 1184.79/297.44 , 23: mark^#(U42(X1, X2, X3)) -> c_23(a__U42^#(mark(X1), X2, X3)) 1184.79/297.44 , 24: a__plus^#(X1, X2) -> c_28(X1, X2) 1184.79/297.44 , 25: a__plus^#(N, s(M)) -> c_29(a__U41^#(a__isNat(M), M, N)) 1184.79/297.44 , 26: a__plus^#(N, 0()) -> c_30(a__U31^#(a__isNat(N), N)) 1184.79/297.44 , 27: a__U41^#(X1, X2, X3) -> c_24(X1, X2, X3) 1184.79/297.44 , 28: a__U41^#(tt(), M, N) -> c_25(a__U42^#(a__isNat(N), M, N)) 1184.79/297.44 , 29: a__U42^#(X1, X2, X3) -> c_26(X1, X2, X3) 1184.79/297.44 , 30: a__U42^#(tt(), M, N) -> c_27(a__plus^#(mark(N), mark(M))) } 1184.79/297.44 1184.79/297.44 We are left with following problem, upon which TcT provides the 1184.79/297.44 certificate MAYBE. 1184.79/297.44 1184.79/297.44 Strict DPs: 1184.79/297.44 { a__U11^#(X1, X2) -> c_1(X1, X2) 1184.79/297.44 , a__U11^#(tt(), V2) -> c_2(a__U12^#(a__isNat(V2))) 1184.79/297.44 , a__U12^#(X) -> c_3(X) 1184.79/297.44 , a__isNat^#(X) -> c_5(X) 1184.79/297.44 , a__isNat^#(s(V1)) -> c_6(a__U21^#(a__isNat(V1))) 1184.79/297.44 , a__isNat^#(plus(V1, V2)) -> c_8(a__U11^#(a__isNat(V1), V2)) 1184.79/297.44 , a__U21^#(X) -> c_9(X) 1184.79/297.44 , a__U31^#(X1, X2) -> c_11(X1, X2) 1184.79/297.44 , a__U31^#(tt(), N) -> c_12(mark^#(N)) 1184.79/297.44 , mark^#(s(X)) -> c_14(mark^#(X)) 1184.79/297.44 , mark^#(plus(X1, X2)) -> c_16(a__plus^#(mark(X1), mark(X2))) 1184.79/297.44 , mark^#(U11(X1, X2)) -> c_17(a__U11^#(mark(X1), X2)) 1184.79/297.44 , mark^#(U12(X)) -> c_18(a__U12^#(mark(X))) 1184.79/297.44 , mark^#(isNat(X)) -> c_19(a__isNat^#(X)) 1184.79/297.44 , mark^#(U21(X)) -> c_20(a__U21^#(mark(X))) 1184.79/297.44 , mark^#(U31(X1, X2)) -> c_21(a__U31^#(mark(X1), X2)) 1184.79/297.44 , mark^#(U41(X1, X2, X3)) -> c_22(a__U41^#(mark(X1), X2, X3)) 1184.79/297.44 , mark^#(U42(X1, X2, X3)) -> c_23(a__U42^#(mark(X1), X2, X3)) 1184.79/297.44 , a__plus^#(X1, X2) -> c_28(X1, X2) 1184.79/297.44 , a__plus^#(N, s(M)) -> c_29(a__U41^#(a__isNat(M), M, N)) 1184.79/297.44 , a__plus^#(N, 0()) -> c_30(a__U31^#(a__isNat(N), N)) 1184.79/297.44 , a__U41^#(X1, X2, X3) -> c_24(X1, X2, X3) 1184.79/297.44 , a__U41^#(tt(), M, N) -> c_25(a__U42^#(a__isNat(N), M, N)) 1184.79/297.44 , a__U42^#(X1, X2, X3) -> c_26(X1, X2, X3) 1184.79/297.44 , a__U42^#(tt(), M, N) -> c_27(a__plus^#(mark(N), mark(M))) } 1184.79/297.44 Strict Trs: 1184.79/297.44 { a__U11(X1, X2) -> U11(X1, X2) 1184.79/297.44 , a__U11(tt(), V2) -> a__U12(a__isNat(V2)) 1184.79/297.44 , a__U12(X) -> U12(X) 1184.79/297.44 , a__U12(tt()) -> tt() 1184.79/297.44 , a__isNat(X) -> isNat(X) 1184.79/297.44 , a__isNat(s(V1)) -> a__U21(a__isNat(V1)) 1184.79/297.44 , a__isNat(0()) -> tt() 1184.79/297.44 , a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) 1184.79/297.44 , a__U21(X) -> U21(X) 1184.79/297.44 , a__U21(tt()) -> tt() 1184.79/297.44 , a__U31(X1, X2) -> U31(X1, X2) 1184.79/297.44 , a__U31(tt(), N) -> mark(N) 1184.79/297.44 , mark(tt()) -> tt() 1184.79/297.44 , mark(s(X)) -> s(mark(X)) 1184.79/297.44 , mark(0()) -> 0() 1184.79/297.44 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1184.79/297.44 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1184.79/297.44 , mark(U12(X)) -> a__U12(mark(X)) 1184.79/297.44 , mark(isNat(X)) -> a__isNat(X) 1184.79/297.44 , mark(U21(X)) -> a__U21(mark(X)) 1184.79/297.44 , mark(U31(X1, X2)) -> a__U31(mark(X1), X2) 1184.79/297.44 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1184.79/297.44 , mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) 1184.79/297.44 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1184.79/297.44 , a__U41(tt(), M, N) -> a__U42(a__isNat(N), M, N) 1184.79/297.44 , a__U42(X1, X2, X3) -> U42(X1, X2, X3) 1184.79/297.44 , a__U42(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1184.79/297.44 , a__plus(X1, X2) -> plus(X1, X2) 1184.79/297.44 , a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) 1184.79/297.44 , a__plus(N, 0()) -> a__U31(a__isNat(N), N) } 1184.79/297.44 Weak DPs: 1184.79/297.44 { a__U12^#(tt()) -> c_4() 1184.79/297.44 , a__isNat^#(0()) -> c_7() 1184.79/297.44 , a__U21^#(tt()) -> c_10() 1184.79/297.44 , mark^#(tt()) -> c_13() 1184.79/297.44 , mark^#(0()) -> c_15() } 1184.79/297.44 Obligation: 1184.79/297.44 runtime complexity 1184.79/297.44 Answer: 1184.79/297.44 MAYBE 1184.79/297.44 1184.79/297.44 Empty strict component of the problem is NOT empty. 1184.79/297.44 1184.79/297.44 1184.79/297.44 Arrrr.. 1185.38/297.89 EOF