MAYBE 1183.53/297.14 MAYBE 1183.53/297.14 1183.53/297.14 We are left with following problem, upon which TcT provides the 1183.53/297.14 certificate MAYBE. 1183.53/297.14 1183.53/297.14 Strict Trs: 1183.53/297.14 { a__U11(X1, X2) -> U11(X1, X2) 1183.53/297.14 , a__U11(tt(), N) -> mark(N) 1183.53/297.14 , mark(tt()) -> tt() 1183.53/297.14 , mark(s(X)) -> s(mark(X)) 1183.53/297.14 , mark(0()) -> 0() 1183.53/297.14 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1183.53/297.14 , mark(isNat(X)) -> a__isNat(X) 1183.53/297.14 , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1183.53/297.14 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1183.53/297.14 , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 1183.53/297.14 , mark(U31(X)) -> a__U31(mark(X)) 1183.53/297.14 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1183.53/297.14 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 1183.53/297.14 , a__U21(X1, X2, X3) -> U21(X1, X2, X3) 1183.53/297.14 , a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1183.53/297.14 , a__plus(X1, X2) -> plus(X1, X2) 1183.53/297.14 , a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) 1183.53/297.14 , a__plus(N, 0()) -> a__U11(a__isNat(N), N) 1183.53/297.14 , a__U31(X) -> U31(X) 1183.53/297.14 , a__U31(tt()) -> 0() 1183.53/297.14 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1183.53/297.14 , a__U41(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 1183.53/297.14 , a__x(X1, X2) -> x(X1, X2) 1183.53/297.14 , a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N) 1183.53/297.14 , a__x(N, 0()) -> a__U31(a__isNat(N)) 1183.53/297.14 , a__and(X1, X2) -> and(X1, X2) 1183.53/297.14 , a__and(tt(), X) -> mark(X) 1183.53/297.14 , a__isNat(X) -> isNat(X) 1183.53/297.14 , a__isNat(s(V1)) -> a__isNat(V1) 1183.53/297.14 , a__isNat(0()) -> tt() 1183.53/297.14 , a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) 1183.53/297.14 , a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) } 1183.53/297.14 Obligation: 1183.53/297.14 runtime complexity 1183.53/297.14 Answer: 1183.53/297.14 MAYBE 1183.53/297.14 1183.53/297.14 None of the processors succeeded. 1183.53/297.14 1183.53/297.14 Details of failed attempt(s): 1183.53/297.14 ----------------------------- 1183.53/297.14 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1183.53/297.14 following reason: 1183.53/297.14 1183.53/297.14 Computation stopped due to timeout after 297.0 seconds. 1183.53/297.14 1183.53/297.14 2) 'Best' failed due to the following reason: 1183.53/297.14 1183.53/297.14 None of the processors succeeded. 1183.53/297.14 1183.53/297.14 Details of failed attempt(s): 1183.53/297.14 ----------------------------- 1183.53/297.14 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1183.53/297.14 seconds)' failed due to the following reason: 1183.53/297.14 1183.53/297.14 Computation stopped due to timeout after 148.0 seconds. 1183.53/297.14 1183.53/297.14 2) 'Best' failed due to the following reason: 1183.53/297.14 1183.53/297.14 None of the processors succeeded. 1183.53/297.14 1183.53/297.14 Details of failed attempt(s): 1183.53/297.14 ----------------------------- 1183.53/297.14 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1183.53/297.14 following reason: 1183.53/297.14 1183.53/297.14 The processor is inapplicable, reason: 1183.53/297.14 Processor only applicable for innermost runtime complexity analysis 1183.53/297.14 1183.53/297.14 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1183.53/297.14 to the following reason: 1183.53/297.14 1183.53/297.14 The processor is inapplicable, reason: 1183.53/297.14 Processor only applicable for innermost runtime complexity analysis 1183.53/297.14 1183.53/297.14 1183.53/297.14 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1183.53/297.14 failed due to the following reason: 1183.53/297.14 1183.53/297.14 None of the processors succeeded. 1183.53/297.14 1183.53/297.14 Details of failed attempt(s): 1183.53/297.14 ----------------------------- 1183.53/297.14 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1183.53/297.14 failed due to the following reason: 1183.53/297.14 1183.53/297.14 match-boundness of the problem could not be verified. 1183.53/297.14 1183.53/297.14 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1183.53/297.14 failed due to the following reason: 1183.53/297.14 1183.53/297.14 match-boundness of the problem could not be verified. 1183.53/297.14 1183.53/297.14 1183.53/297.14 1183.53/297.14 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1183.53/297.14 the following reason: 1183.53/297.14 1183.53/297.14 We add the following weak dependency pairs: 1183.53/297.14 1183.53/297.14 Strict DPs: 1183.53/297.14 { a__U11^#(X1, X2) -> c_1(X1, X2) 1183.53/297.14 , a__U11^#(tt(), N) -> c_2(mark^#(N)) 1183.53/297.14 , mark^#(tt()) -> c_3() 1183.53/297.14 , mark^#(s(X)) -> c_4(mark^#(X)) 1183.53/297.14 , mark^#(0()) -> c_5() 1183.53/297.14 , mark^#(plus(X1, X2)) -> c_6(a__plus^#(mark(X1), mark(X2))) 1183.53/297.14 , mark^#(isNat(X)) -> c_7(a__isNat^#(X)) 1183.53/297.14 , mark^#(x(X1, X2)) -> c_8(a__x^#(mark(X1), mark(X2))) 1183.53/297.14 , mark^#(U11(X1, X2)) -> c_9(a__U11^#(mark(X1), X2)) 1183.53/297.14 , mark^#(U21(X1, X2, X3)) -> c_10(a__U21^#(mark(X1), X2, X3)) 1183.53/297.14 , mark^#(U31(X)) -> c_11(a__U31^#(mark(X))) 1183.53/297.14 , mark^#(U41(X1, X2, X3)) -> c_12(a__U41^#(mark(X1), X2, X3)) 1183.53/297.14 , mark^#(and(X1, X2)) -> c_13(a__and^#(mark(X1), X2)) 1183.53/297.14 , a__plus^#(X1, X2) -> c_16(X1, X2) 1183.53/297.14 , a__plus^#(N, s(M)) -> 1183.53/297.14 c_17(a__U21^#(a__and(a__isNat(M), isNat(N)), M, N)) 1183.53/297.14 , a__plus^#(N, 0()) -> c_18(a__U11^#(a__isNat(N), N)) 1183.53/297.14 , a__isNat^#(X) -> c_28(X) 1183.53/297.14 , a__isNat^#(s(V1)) -> c_29(a__isNat^#(V1)) 1183.53/297.14 , a__isNat^#(0()) -> c_30() 1183.53/297.14 , a__isNat^#(plus(V1, V2)) -> 1183.53/297.14 c_31(a__and^#(a__isNat(V1), isNat(V2))) 1183.53/297.14 , a__isNat^#(x(V1, V2)) -> c_32(a__and^#(a__isNat(V1), isNat(V2))) 1183.53/297.14 , a__x^#(X1, X2) -> c_23(X1, X2) 1183.53/297.14 , a__x^#(N, s(M)) -> 1183.53/297.14 c_24(a__U41^#(a__and(a__isNat(M), isNat(N)), M, N)) 1183.53/297.14 , a__x^#(N, 0()) -> c_25(a__U31^#(a__isNat(N))) 1183.53/297.14 , a__U21^#(X1, X2, X3) -> c_14(X1, X2, X3) 1183.53/297.14 , a__U21^#(tt(), M, N) -> c_15(a__plus^#(mark(N), mark(M))) 1183.53/297.14 , a__U31^#(X) -> c_19(X) 1183.53/297.14 , a__U31^#(tt()) -> c_20() 1183.53/297.14 , a__U41^#(X1, X2, X3) -> c_21(X1, X2, X3) 1183.53/297.14 , a__U41^#(tt(), M, N) -> 1183.53/297.14 c_22(a__plus^#(a__x(mark(N), mark(M)), mark(N))) 1183.53/297.14 , a__and^#(X1, X2) -> c_26(X1, X2) 1183.53/297.14 , a__and^#(tt(), X) -> c_27(mark^#(X)) } 1183.53/297.14 1183.53/297.14 and mark the set of starting terms. 1183.53/297.14 1183.53/297.14 We are left with following problem, upon which TcT provides the 1183.53/297.14 certificate MAYBE. 1183.53/297.14 1183.53/297.14 Strict DPs: 1183.53/297.14 { a__U11^#(X1, X2) -> c_1(X1, X2) 1183.53/297.14 , a__U11^#(tt(), N) -> c_2(mark^#(N)) 1183.53/297.14 , mark^#(tt()) -> c_3() 1183.53/297.14 , mark^#(s(X)) -> c_4(mark^#(X)) 1183.53/297.14 , mark^#(0()) -> c_5() 1183.53/297.14 , mark^#(plus(X1, X2)) -> c_6(a__plus^#(mark(X1), mark(X2))) 1183.53/297.14 , mark^#(isNat(X)) -> c_7(a__isNat^#(X)) 1183.53/297.14 , mark^#(x(X1, X2)) -> c_8(a__x^#(mark(X1), mark(X2))) 1183.53/297.14 , mark^#(U11(X1, X2)) -> c_9(a__U11^#(mark(X1), X2)) 1183.53/297.14 , mark^#(U21(X1, X2, X3)) -> c_10(a__U21^#(mark(X1), X2, X3)) 1183.53/297.14 , mark^#(U31(X)) -> c_11(a__U31^#(mark(X))) 1183.53/297.14 , mark^#(U41(X1, X2, X3)) -> c_12(a__U41^#(mark(X1), X2, X3)) 1183.53/297.14 , mark^#(and(X1, X2)) -> c_13(a__and^#(mark(X1), X2)) 1183.53/297.14 , a__plus^#(X1, X2) -> c_16(X1, X2) 1183.53/297.14 , a__plus^#(N, s(M)) -> 1183.53/297.14 c_17(a__U21^#(a__and(a__isNat(M), isNat(N)), M, N)) 1183.53/297.14 , a__plus^#(N, 0()) -> c_18(a__U11^#(a__isNat(N), N)) 1183.53/297.14 , a__isNat^#(X) -> c_28(X) 1183.53/297.14 , a__isNat^#(s(V1)) -> c_29(a__isNat^#(V1)) 1183.53/297.14 , a__isNat^#(0()) -> c_30() 1183.53/297.14 , a__isNat^#(plus(V1, V2)) -> 1183.53/297.14 c_31(a__and^#(a__isNat(V1), isNat(V2))) 1183.53/297.14 , a__isNat^#(x(V1, V2)) -> c_32(a__and^#(a__isNat(V1), isNat(V2))) 1183.53/297.14 , a__x^#(X1, X2) -> c_23(X1, X2) 1183.53/297.14 , a__x^#(N, s(M)) -> 1183.53/297.14 c_24(a__U41^#(a__and(a__isNat(M), isNat(N)), M, N)) 1183.53/297.14 , a__x^#(N, 0()) -> c_25(a__U31^#(a__isNat(N))) 1183.53/297.14 , a__U21^#(X1, X2, X3) -> c_14(X1, X2, X3) 1183.53/297.14 , a__U21^#(tt(), M, N) -> c_15(a__plus^#(mark(N), mark(M))) 1183.53/297.14 , a__U31^#(X) -> c_19(X) 1183.53/297.14 , a__U31^#(tt()) -> c_20() 1183.53/297.14 , a__U41^#(X1, X2, X3) -> c_21(X1, X2, X3) 1183.53/297.14 , a__U41^#(tt(), M, N) -> 1183.53/297.14 c_22(a__plus^#(a__x(mark(N), mark(M)), mark(N))) 1183.53/297.14 , a__and^#(X1, X2) -> c_26(X1, X2) 1183.53/297.14 , a__and^#(tt(), X) -> c_27(mark^#(X)) } 1183.53/297.14 Strict Trs: 1183.53/297.14 { a__U11(X1, X2) -> U11(X1, X2) 1183.53/297.14 , a__U11(tt(), N) -> mark(N) 1183.53/297.14 , mark(tt()) -> tt() 1183.53/297.14 , mark(s(X)) -> s(mark(X)) 1183.53/297.14 , mark(0()) -> 0() 1183.53/297.14 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1183.53/297.14 , mark(isNat(X)) -> a__isNat(X) 1183.53/297.14 , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1183.53/297.14 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1183.53/297.14 , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 1183.53/297.14 , mark(U31(X)) -> a__U31(mark(X)) 1183.53/297.14 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1183.53/297.14 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 1183.53/297.14 , a__U21(X1, X2, X3) -> U21(X1, X2, X3) 1183.53/297.14 , a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1183.53/297.14 , a__plus(X1, X2) -> plus(X1, X2) 1183.53/297.14 , a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) 1183.53/297.14 , a__plus(N, 0()) -> a__U11(a__isNat(N), N) 1183.53/297.14 , a__U31(X) -> U31(X) 1183.53/297.14 , a__U31(tt()) -> 0() 1183.53/297.14 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1183.53/297.14 , a__U41(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 1183.53/297.14 , a__x(X1, X2) -> x(X1, X2) 1183.53/297.14 , a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N) 1183.53/297.14 , a__x(N, 0()) -> a__U31(a__isNat(N)) 1183.53/297.14 , a__and(X1, X2) -> and(X1, X2) 1183.53/297.14 , a__and(tt(), X) -> mark(X) 1183.53/297.14 , a__isNat(X) -> isNat(X) 1183.53/297.14 , a__isNat(s(V1)) -> a__isNat(V1) 1183.53/297.14 , a__isNat(0()) -> tt() 1183.53/297.14 , a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) 1183.53/297.14 , a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) } 1183.53/297.14 Obligation: 1183.53/297.14 runtime complexity 1183.53/297.14 Answer: 1183.53/297.14 MAYBE 1183.53/297.14 1183.53/297.14 We estimate the number of application of {3,5,19,28} by 1183.53/297.14 applications of Pre({3,5,19,28}) = 1183.53/297.14 {1,2,4,7,11,14,17,18,22,24,25,27,29,31,32}. Here rules are labeled 1183.53/297.14 as follows: 1183.53/297.14 1183.53/297.14 DPs: 1183.53/297.14 { 1: a__U11^#(X1, X2) -> c_1(X1, X2) 1183.53/297.14 , 2: a__U11^#(tt(), N) -> c_2(mark^#(N)) 1183.53/297.14 , 3: mark^#(tt()) -> c_3() 1183.53/297.14 , 4: mark^#(s(X)) -> c_4(mark^#(X)) 1183.53/297.14 , 5: mark^#(0()) -> c_5() 1183.53/297.14 , 6: mark^#(plus(X1, X2)) -> c_6(a__plus^#(mark(X1), mark(X2))) 1183.53/297.14 , 7: mark^#(isNat(X)) -> c_7(a__isNat^#(X)) 1183.53/297.14 , 8: mark^#(x(X1, X2)) -> c_8(a__x^#(mark(X1), mark(X2))) 1183.53/297.14 , 9: mark^#(U11(X1, X2)) -> c_9(a__U11^#(mark(X1), X2)) 1183.53/297.14 , 10: mark^#(U21(X1, X2, X3)) -> c_10(a__U21^#(mark(X1), X2, X3)) 1183.53/297.14 , 11: mark^#(U31(X)) -> c_11(a__U31^#(mark(X))) 1183.53/297.14 , 12: mark^#(U41(X1, X2, X3)) -> c_12(a__U41^#(mark(X1), X2, X3)) 1183.53/297.14 , 13: mark^#(and(X1, X2)) -> c_13(a__and^#(mark(X1), X2)) 1183.53/297.14 , 14: a__plus^#(X1, X2) -> c_16(X1, X2) 1183.53/297.14 , 15: a__plus^#(N, s(M)) -> 1183.53/297.14 c_17(a__U21^#(a__and(a__isNat(M), isNat(N)), M, N)) 1183.53/297.14 , 16: a__plus^#(N, 0()) -> c_18(a__U11^#(a__isNat(N), N)) 1183.53/297.14 , 17: a__isNat^#(X) -> c_28(X) 1183.53/297.14 , 18: a__isNat^#(s(V1)) -> c_29(a__isNat^#(V1)) 1183.53/297.14 , 19: a__isNat^#(0()) -> c_30() 1183.53/297.14 , 20: a__isNat^#(plus(V1, V2)) -> 1183.53/297.14 c_31(a__and^#(a__isNat(V1), isNat(V2))) 1183.53/297.14 , 21: a__isNat^#(x(V1, V2)) -> 1183.53/297.14 c_32(a__and^#(a__isNat(V1), isNat(V2))) 1183.53/297.14 , 22: a__x^#(X1, X2) -> c_23(X1, X2) 1183.53/297.14 , 23: a__x^#(N, s(M)) -> 1183.53/297.14 c_24(a__U41^#(a__and(a__isNat(M), isNat(N)), M, N)) 1183.53/297.14 , 24: a__x^#(N, 0()) -> c_25(a__U31^#(a__isNat(N))) 1183.53/297.14 , 25: a__U21^#(X1, X2, X3) -> c_14(X1, X2, X3) 1183.53/297.14 , 26: a__U21^#(tt(), M, N) -> c_15(a__plus^#(mark(N), mark(M))) 1183.53/297.14 , 27: a__U31^#(X) -> c_19(X) 1183.53/297.14 , 28: a__U31^#(tt()) -> c_20() 1183.53/297.14 , 29: a__U41^#(X1, X2, X3) -> c_21(X1, X2, X3) 1183.53/297.14 , 30: a__U41^#(tt(), M, N) -> 1183.53/297.14 c_22(a__plus^#(a__x(mark(N), mark(M)), mark(N))) 1183.53/297.14 , 31: a__and^#(X1, X2) -> c_26(X1, X2) 1183.53/297.14 , 32: a__and^#(tt(), X) -> c_27(mark^#(X)) } 1183.53/297.14 1183.53/297.14 We are left with following problem, upon which TcT provides the 1183.53/297.14 certificate MAYBE. 1183.53/297.14 1183.53/297.14 Strict DPs: 1183.53/297.14 { a__U11^#(X1, X2) -> c_1(X1, X2) 1183.53/297.14 , a__U11^#(tt(), N) -> c_2(mark^#(N)) 1183.53/297.14 , mark^#(s(X)) -> c_4(mark^#(X)) 1183.53/297.14 , mark^#(plus(X1, X2)) -> c_6(a__plus^#(mark(X1), mark(X2))) 1183.53/297.14 , mark^#(isNat(X)) -> c_7(a__isNat^#(X)) 1183.53/297.14 , mark^#(x(X1, X2)) -> c_8(a__x^#(mark(X1), mark(X2))) 1183.53/297.14 , mark^#(U11(X1, X2)) -> c_9(a__U11^#(mark(X1), X2)) 1183.53/297.14 , mark^#(U21(X1, X2, X3)) -> c_10(a__U21^#(mark(X1), X2, X3)) 1183.53/297.14 , mark^#(U31(X)) -> c_11(a__U31^#(mark(X))) 1183.53/297.14 , mark^#(U41(X1, X2, X3)) -> c_12(a__U41^#(mark(X1), X2, X3)) 1183.53/297.14 , mark^#(and(X1, X2)) -> c_13(a__and^#(mark(X1), X2)) 1183.53/297.14 , a__plus^#(X1, X2) -> c_16(X1, X2) 1183.53/297.14 , a__plus^#(N, s(M)) -> 1183.53/297.14 c_17(a__U21^#(a__and(a__isNat(M), isNat(N)), M, N)) 1183.53/297.14 , a__plus^#(N, 0()) -> c_18(a__U11^#(a__isNat(N), N)) 1183.53/297.14 , a__isNat^#(X) -> c_28(X) 1183.53/297.14 , a__isNat^#(s(V1)) -> c_29(a__isNat^#(V1)) 1183.53/297.14 , a__isNat^#(plus(V1, V2)) -> 1183.53/297.14 c_31(a__and^#(a__isNat(V1), isNat(V2))) 1183.53/297.14 , a__isNat^#(x(V1, V2)) -> c_32(a__and^#(a__isNat(V1), isNat(V2))) 1183.53/297.14 , a__x^#(X1, X2) -> c_23(X1, X2) 1183.53/297.14 , a__x^#(N, s(M)) -> 1183.53/297.14 c_24(a__U41^#(a__and(a__isNat(M), isNat(N)), M, N)) 1183.53/297.14 , a__x^#(N, 0()) -> c_25(a__U31^#(a__isNat(N))) 1183.53/297.14 , a__U21^#(X1, X2, X3) -> c_14(X1, X2, X3) 1183.53/297.14 , a__U21^#(tt(), M, N) -> c_15(a__plus^#(mark(N), mark(M))) 1183.53/297.14 , a__U31^#(X) -> c_19(X) 1183.53/297.14 , a__U41^#(X1, X2, X3) -> c_21(X1, X2, X3) 1183.53/297.14 , a__U41^#(tt(), M, N) -> 1183.53/297.14 c_22(a__plus^#(a__x(mark(N), mark(M)), mark(N))) 1183.53/297.14 , a__and^#(X1, X2) -> c_26(X1, X2) 1183.53/297.14 , a__and^#(tt(), X) -> c_27(mark^#(X)) } 1183.53/297.14 Strict Trs: 1183.53/297.14 { a__U11(X1, X2) -> U11(X1, X2) 1183.53/297.14 , a__U11(tt(), N) -> mark(N) 1183.53/297.14 , mark(tt()) -> tt() 1183.53/297.14 , mark(s(X)) -> s(mark(X)) 1183.53/297.14 , mark(0()) -> 0() 1183.53/297.14 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1183.53/297.14 , mark(isNat(X)) -> a__isNat(X) 1183.53/297.14 , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1183.53/297.14 , mark(U11(X1, X2)) -> a__U11(mark(X1), X2) 1183.53/297.14 , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 1183.53/297.14 , mark(U31(X)) -> a__U31(mark(X)) 1183.53/297.14 , mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) 1183.53/297.14 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 1183.53/297.14 , a__U21(X1, X2, X3) -> U21(X1, X2, X3) 1183.53/297.14 , a__U21(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1183.53/297.14 , a__plus(X1, X2) -> plus(X1, X2) 1183.53/297.14 , a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) 1183.53/297.14 , a__plus(N, 0()) -> a__U11(a__isNat(N), N) 1183.53/297.14 , a__U31(X) -> U31(X) 1183.53/297.14 , a__U31(tt()) -> 0() 1183.53/297.14 , a__U41(X1, X2, X3) -> U41(X1, X2, X3) 1183.53/297.14 , a__U41(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 1183.53/297.14 , a__x(X1, X2) -> x(X1, X2) 1183.53/297.14 , a__x(N, s(M)) -> a__U41(a__and(a__isNat(M), isNat(N)), M, N) 1183.53/297.14 , a__x(N, 0()) -> a__U31(a__isNat(N)) 1183.53/297.14 , a__and(X1, X2) -> and(X1, X2) 1183.53/297.14 , a__and(tt(), X) -> mark(X) 1183.53/297.14 , a__isNat(X) -> isNat(X) 1183.53/297.14 , a__isNat(s(V1)) -> a__isNat(V1) 1183.53/297.14 , a__isNat(0()) -> tt() 1183.53/297.14 , a__isNat(plus(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) 1183.53/297.14 , a__isNat(x(V1, V2)) -> a__and(a__isNat(V1), isNat(V2)) } 1183.53/297.14 Weak DPs: 1183.53/297.14 { mark^#(tt()) -> c_3() 1183.53/297.14 , mark^#(0()) -> c_5() 1183.53/297.14 , a__isNat^#(0()) -> c_30() 1183.53/297.14 , a__U31^#(tt()) -> c_20() } 1183.53/297.14 Obligation: 1183.53/297.14 runtime complexity 1183.53/297.14 Answer: 1183.53/297.14 MAYBE 1183.53/297.14 1183.53/297.14 Empty strict component of the problem is NOT empty. 1183.53/297.14 1183.53/297.14 1183.53/297.14 Arrrr.. 1184.34/297.81 EOF