MAYBE 1168.85/297.05 MAYBE 1168.85/297.05 1168.85/297.05 We are left with following problem, upon which TcT provides the 1168.85/297.05 certificate MAYBE. 1168.85/297.05 1168.85/297.05 Strict Trs: 1168.85/297.05 { a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1168.85/297.05 , a__U11(tt(), M, N) -> a__U12(tt(), M, N) 1168.85/297.05 , a__U12(X1, X2, X3) -> U12(X1, X2, X3) 1168.85/297.05 , a__U12(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1168.85/297.05 , a__plus(X1, X2) -> plus(X1, X2) 1168.85/297.05 , a__plus(N, s(M)) -> a__U11(tt(), M, N) 1168.85/297.05 , a__plus(N, 0()) -> mark(N) 1168.85/297.05 , mark(tt()) -> tt() 1168.85/297.05 , mark(s(X)) -> s(mark(X)) 1168.85/297.05 , mark(0()) -> 0() 1168.85/297.05 , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1168.85/297.05 , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 1168.85/297.05 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1168.85/297.05 , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 1168.85/297.05 , mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) 1168.85/297.05 , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1168.85/297.05 , a__U21(X1, X2, X3) -> U21(X1, X2, X3) 1168.85/297.05 , a__U21(tt(), M, N) -> a__U22(tt(), M, N) 1168.85/297.05 , a__U22(X1, X2, X3) -> U22(X1, X2, X3) 1168.85/297.05 , a__U22(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 1168.85/297.05 , a__x(X1, X2) -> x(X1, X2) 1168.85/297.05 , a__x(N, s(M)) -> a__U21(tt(), M, N) 1168.85/297.05 , a__x(N, 0()) -> 0() } 1168.85/297.05 Obligation: 1168.85/297.05 runtime complexity 1168.85/297.05 Answer: 1168.85/297.05 MAYBE 1168.85/297.05 1168.85/297.05 None of the processors succeeded. 1168.85/297.05 1168.85/297.05 Details of failed attempt(s): 1168.85/297.05 ----------------------------- 1168.85/297.05 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1168.85/297.05 following reason: 1168.85/297.05 1168.85/297.05 Computation stopped due to timeout after 297.0 seconds. 1168.85/297.05 1168.85/297.05 2) 'Best' failed due to the following reason: 1168.85/297.05 1168.85/297.05 None of the processors succeeded. 1168.85/297.05 1168.85/297.05 Details of failed attempt(s): 1168.85/297.05 ----------------------------- 1168.85/297.05 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1168.85/297.05 seconds)' failed due to the following reason: 1168.85/297.05 1168.85/297.05 Computation stopped due to timeout after 148.0 seconds. 1168.85/297.05 1168.85/297.05 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1168.85/297.05 failed due to the following reason: 1168.85/297.05 1168.85/297.05 None of the processors succeeded. 1168.85/297.05 1168.85/297.05 Details of failed attempt(s): 1168.85/297.05 ----------------------------- 1168.85/297.05 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1168.85/297.05 failed due to the following reason: 1168.85/297.05 1168.85/297.05 match-boundness of the problem could not be verified. 1168.85/297.05 1168.85/297.05 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1168.85/297.05 failed due to the following reason: 1168.85/297.05 1168.85/297.05 match-boundness of the problem could not be verified. 1168.85/297.05 1168.85/297.05 1168.85/297.05 3) 'Best' failed due to the following reason: 1168.85/297.05 1168.85/297.05 None of the processors succeeded. 1168.85/297.05 1168.85/297.05 Details of failed attempt(s): 1168.85/297.05 ----------------------------- 1168.85/297.05 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1168.85/297.05 following reason: 1168.85/297.05 1168.85/297.05 The processor is inapplicable, reason: 1168.85/297.05 Processor only applicable for innermost runtime complexity analysis 1168.85/297.05 1168.85/297.05 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1168.85/297.05 to the following reason: 1168.85/297.05 1168.85/297.05 The processor is inapplicable, reason: 1168.85/297.05 Processor only applicable for innermost runtime complexity analysis 1168.85/297.05 1168.85/297.05 1168.85/297.05 1168.85/297.05 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1168.85/297.05 the following reason: 1168.85/297.05 1168.85/297.05 We add the following weak dependency pairs: 1168.85/297.05 1168.85/297.05 Strict DPs: 1168.85/297.05 { a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3) 1168.85/297.05 , a__U11^#(tt(), M, N) -> c_2(a__U12^#(tt(), M, N)) 1168.85/297.05 , a__U12^#(X1, X2, X3) -> c_3(X1, X2, X3) 1168.85/297.05 , a__U12^#(tt(), M, N) -> c_4(a__plus^#(mark(N), mark(M))) 1168.85/297.05 , a__plus^#(X1, X2) -> c_5(X1, X2) 1168.85/297.05 , a__plus^#(N, s(M)) -> c_6(a__U11^#(tt(), M, N)) 1168.85/297.05 , a__plus^#(N, 0()) -> c_7(mark^#(N)) 1168.85/297.05 , mark^#(tt()) -> c_8() 1168.85/297.05 , mark^#(s(X)) -> c_9(mark^#(X)) 1168.85/297.05 , mark^#(0()) -> c_10() 1168.85/297.05 , mark^#(U11(X1, X2, X3)) -> c_11(a__U11^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(U12(X1, X2, X3)) -> c_12(a__U12^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(plus(X1, X2)) -> c_13(a__plus^#(mark(X1), mark(X2))) 1168.85/297.05 , mark^#(U21(X1, X2, X3)) -> c_14(a__U21^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(U22(X1, X2, X3)) -> c_15(a__U22^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(x(X1, X2)) -> c_16(a__x^#(mark(X1), mark(X2))) 1168.85/297.05 , a__U21^#(X1, X2, X3) -> c_17(X1, X2, X3) 1168.85/297.05 , a__U21^#(tt(), M, N) -> c_18(a__U22^#(tt(), M, N)) 1168.85/297.05 , a__U22^#(X1, X2, X3) -> c_19(X1, X2, X3) 1168.85/297.05 , a__U22^#(tt(), M, N) -> 1168.85/297.05 c_20(a__plus^#(a__x(mark(N), mark(M)), mark(N))) 1168.85/297.05 , a__x^#(X1, X2) -> c_21(X1, X2) 1168.85/297.05 , a__x^#(N, s(M)) -> c_22(a__U21^#(tt(), M, N)) 1168.85/297.05 , a__x^#(N, 0()) -> c_23() } 1168.85/297.05 1168.85/297.05 and mark the set of starting terms. 1168.85/297.05 1168.85/297.05 We are left with following problem, upon which TcT provides the 1168.85/297.05 certificate MAYBE. 1168.85/297.05 1168.85/297.05 Strict DPs: 1168.85/297.05 { a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3) 1168.85/297.05 , a__U11^#(tt(), M, N) -> c_2(a__U12^#(tt(), M, N)) 1168.85/297.05 , a__U12^#(X1, X2, X3) -> c_3(X1, X2, X3) 1168.85/297.05 , a__U12^#(tt(), M, N) -> c_4(a__plus^#(mark(N), mark(M))) 1168.85/297.05 , a__plus^#(X1, X2) -> c_5(X1, X2) 1168.85/297.05 , a__plus^#(N, s(M)) -> c_6(a__U11^#(tt(), M, N)) 1168.85/297.05 , a__plus^#(N, 0()) -> c_7(mark^#(N)) 1168.85/297.05 , mark^#(tt()) -> c_8() 1168.85/297.05 , mark^#(s(X)) -> c_9(mark^#(X)) 1168.85/297.05 , mark^#(0()) -> c_10() 1168.85/297.05 , mark^#(U11(X1, X2, X3)) -> c_11(a__U11^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(U12(X1, X2, X3)) -> c_12(a__U12^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(plus(X1, X2)) -> c_13(a__plus^#(mark(X1), mark(X2))) 1168.85/297.05 , mark^#(U21(X1, X2, X3)) -> c_14(a__U21^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(U22(X1, X2, X3)) -> c_15(a__U22^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(x(X1, X2)) -> c_16(a__x^#(mark(X1), mark(X2))) 1168.85/297.05 , a__U21^#(X1, X2, X3) -> c_17(X1, X2, X3) 1168.85/297.05 , a__U21^#(tt(), M, N) -> c_18(a__U22^#(tt(), M, N)) 1168.85/297.05 , a__U22^#(X1, X2, X3) -> c_19(X1, X2, X3) 1168.85/297.05 , a__U22^#(tt(), M, N) -> 1168.85/297.05 c_20(a__plus^#(a__x(mark(N), mark(M)), mark(N))) 1168.85/297.05 , a__x^#(X1, X2) -> c_21(X1, X2) 1168.85/297.05 , a__x^#(N, s(M)) -> c_22(a__U21^#(tt(), M, N)) 1168.85/297.05 , a__x^#(N, 0()) -> c_23() } 1168.85/297.05 Strict Trs: 1168.85/297.05 { a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1168.85/297.05 , a__U11(tt(), M, N) -> a__U12(tt(), M, N) 1168.85/297.05 , a__U12(X1, X2, X3) -> U12(X1, X2, X3) 1168.85/297.05 , a__U12(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1168.85/297.05 , a__plus(X1, X2) -> plus(X1, X2) 1168.85/297.05 , a__plus(N, s(M)) -> a__U11(tt(), M, N) 1168.85/297.05 , a__plus(N, 0()) -> mark(N) 1168.85/297.05 , mark(tt()) -> tt() 1168.85/297.05 , mark(s(X)) -> s(mark(X)) 1168.85/297.05 , mark(0()) -> 0() 1168.85/297.05 , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1168.85/297.05 , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 1168.85/297.05 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1168.85/297.05 , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 1168.85/297.05 , mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) 1168.85/297.05 , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1168.85/297.05 , a__U21(X1, X2, X3) -> U21(X1, X2, X3) 1168.85/297.05 , a__U21(tt(), M, N) -> a__U22(tt(), M, N) 1168.85/297.05 , a__U22(X1, X2, X3) -> U22(X1, X2, X3) 1168.85/297.05 , a__U22(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 1168.85/297.05 , a__x(X1, X2) -> x(X1, X2) 1168.85/297.05 , a__x(N, s(M)) -> a__U21(tt(), M, N) 1168.85/297.05 , a__x(N, 0()) -> 0() } 1168.85/297.05 Obligation: 1168.85/297.05 runtime complexity 1168.85/297.05 Answer: 1168.85/297.05 MAYBE 1168.85/297.05 1168.85/297.05 We estimate the number of application of {8,10,23} by applications 1168.85/297.05 of Pre({8,10,23}) = {1,3,5,7,9,16,17,19,21}. Here rules are labeled 1168.85/297.05 as follows: 1168.85/297.05 1168.85/297.05 DPs: 1168.85/297.05 { 1: a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3) 1168.85/297.05 , 2: a__U11^#(tt(), M, N) -> c_2(a__U12^#(tt(), M, N)) 1168.85/297.05 , 3: a__U12^#(X1, X2, X3) -> c_3(X1, X2, X3) 1168.85/297.05 , 4: a__U12^#(tt(), M, N) -> c_4(a__plus^#(mark(N), mark(M))) 1168.85/297.05 , 5: a__plus^#(X1, X2) -> c_5(X1, X2) 1168.85/297.05 , 6: a__plus^#(N, s(M)) -> c_6(a__U11^#(tt(), M, N)) 1168.85/297.05 , 7: a__plus^#(N, 0()) -> c_7(mark^#(N)) 1168.85/297.05 , 8: mark^#(tt()) -> c_8() 1168.85/297.05 , 9: mark^#(s(X)) -> c_9(mark^#(X)) 1168.85/297.05 , 10: mark^#(0()) -> c_10() 1168.85/297.05 , 11: mark^#(U11(X1, X2, X3)) -> c_11(a__U11^#(mark(X1), X2, X3)) 1168.85/297.05 , 12: mark^#(U12(X1, X2, X3)) -> c_12(a__U12^#(mark(X1), X2, X3)) 1168.85/297.05 , 13: mark^#(plus(X1, X2)) -> c_13(a__plus^#(mark(X1), mark(X2))) 1168.85/297.05 , 14: mark^#(U21(X1, X2, X3)) -> c_14(a__U21^#(mark(X1), X2, X3)) 1168.85/297.05 , 15: mark^#(U22(X1, X2, X3)) -> c_15(a__U22^#(mark(X1), X2, X3)) 1168.85/297.05 , 16: mark^#(x(X1, X2)) -> c_16(a__x^#(mark(X1), mark(X2))) 1168.85/297.05 , 17: a__U21^#(X1, X2, X3) -> c_17(X1, X2, X3) 1168.85/297.05 , 18: a__U21^#(tt(), M, N) -> c_18(a__U22^#(tt(), M, N)) 1168.85/297.05 , 19: a__U22^#(X1, X2, X3) -> c_19(X1, X2, X3) 1168.85/297.05 , 20: a__U22^#(tt(), M, N) -> 1168.85/297.05 c_20(a__plus^#(a__x(mark(N), mark(M)), mark(N))) 1168.85/297.05 , 21: a__x^#(X1, X2) -> c_21(X1, X2) 1168.85/297.05 , 22: a__x^#(N, s(M)) -> c_22(a__U21^#(tt(), M, N)) 1168.85/297.05 , 23: a__x^#(N, 0()) -> c_23() } 1168.85/297.05 1168.85/297.05 We are left with following problem, upon which TcT provides the 1168.85/297.05 certificate MAYBE. 1168.85/297.05 1168.85/297.05 Strict DPs: 1168.85/297.05 { a__U11^#(X1, X2, X3) -> c_1(X1, X2, X3) 1168.85/297.05 , a__U11^#(tt(), M, N) -> c_2(a__U12^#(tt(), M, N)) 1168.85/297.05 , a__U12^#(X1, X2, X3) -> c_3(X1, X2, X3) 1168.85/297.05 , a__U12^#(tt(), M, N) -> c_4(a__plus^#(mark(N), mark(M))) 1168.85/297.05 , a__plus^#(X1, X2) -> c_5(X1, X2) 1168.85/297.05 , a__plus^#(N, s(M)) -> c_6(a__U11^#(tt(), M, N)) 1168.85/297.05 , a__plus^#(N, 0()) -> c_7(mark^#(N)) 1168.85/297.05 , mark^#(s(X)) -> c_9(mark^#(X)) 1168.85/297.05 , mark^#(U11(X1, X2, X3)) -> c_11(a__U11^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(U12(X1, X2, X3)) -> c_12(a__U12^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(plus(X1, X2)) -> c_13(a__plus^#(mark(X1), mark(X2))) 1168.85/297.05 , mark^#(U21(X1, X2, X3)) -> c_14(a__U21^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(U22(X1, X2, X3)) -> c_15(a__U22^#(mark(X1), X2, X3)) 1168.85/297.05 , mark^#(x(X1, X2)) -> c_16(a__x^#(mark(X1), mark(X2))) 1168.85/297.05 , a__U21^#(X1, X2, X3) -> c_17(X1, X2, X3) 1168.85/297.05 , a__U21^#(tt(), M, N) -> c_18(a__U22^#(tt(), M, N)) 1168.85/297.05 , a__U22^#(X1, X2, X3) -> c_19(X1, X2, X3) 1168.85/297.05 , a__U22^#(tt(), M, N) -> 1168.85/297.05 c_20(a__plus^#(a__x(mark(N), mark(M)), mark(N))) 1168.85/297.05 , a__x^#(X1, X2) -> c_21(X1, X2) 1168.85/297.05 , a__x^#(N, s(M)) -> c_22(a__U21^#(tt(), M, N)) } 1168.85/297.05 Strict Trs: 1168.85/297.05 { a__U11(X1, X2, X3) -> U11(X1, X2, X3) 1168.85/297.05 , a__U11(tt(), M, N) -> a__U12(tt(), M, N) 1168.85/297.05 , a__U12(X1, X2, X3) -> U12(X1, X2, X3) 1168.85/297.05 , a__U12(tt(), M, N) -> s(a__plus(mark(N), mark(M))) 1168.85/297.05 , a__plus(X1, X2) -> plus(X1, X2) 1168.85/297.05 , a__plus(N, s(M)) -> a__U11(tt(), M, N) 1168.85/297.05 , a__plus(N, 0()) -> mark(N) 1168.85/297.05 , mark(tt()) -> tt() 1168.85/297.05 , mark(s(X)) -> s(mark(X)) 1168.85/297.05 , mark(0()) -> 0() 1168.85/297.05 , mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) 1168.85/297.05 , mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) 1168.85/297.05 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1168.85/297.05 , mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) 1168.85/297.05 , mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) 1168.85/297.05 , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1168.85/297.05 , a__U21(X1, X2, X3) -> U21(X1, X2, X3) 1168.85/297.05 , a__U21(tt(), M, N) -> a__U22(tt(), M, N) 1168.85/297.05 , a__U22(X1, X2, X3) -> U22(X1, X2, X3) 1168.85/297.05 , a__U22(tt(), M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) 1168.85/297.05 , a__x(X1, X2) -> x(X1, X2) 1168.85/297.05 , a__x(N, s(M)) -> a__U21(tt(), M, N) 1168.85/297.05 , a__x(N, 0()) -> 0() } 1168.85/297.05 Weak DPs: 1168.85/297.05 { mark^#(tt()) -> c_8() 1168.85/297.05 , mark^#(0()) -> c_10() 1168.85/297.05 , a__x^#(N, 0()) -> c_23() } 1168.85/297.05 Obligation: 1168.85/297.05 runtime complexity 1168.85/297.05 Answer: 1168.85/297.05 MAYBE 1168.85/297.05 1168.85/297.05 Empty strict component of the problem is NOT empty. 1168.85/297.05 1168.85/297.05 1168.85/297.05 Arrrr.. 1169.58/297.67 EOF