MAYBE 1158.55/297.03 MAYBE 1158.55/297.03 1158.55/297.03 We are left with following problem, upon which TcT provides the 1158.55/297.03 certificate MAYBE. 1158.55/297.03 1158.55/297.03 Strict Trs: 1158.55/297.03 { a__and(X1, X2) -> and(X1, X2) 1158.55/297.03 , a__and(tt(), X) -> mark(X) 1158.55/297.03 , mark(tt()) -> tt() 1158.55/297.03 , mark(0()) -> 0() 1158.55/297.03 , mark(s(X)) -> s(mark(X)) 1158.55/297.03 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 1158.55/297.03 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1158.55/297.03 , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1158.55/297.03 , a__plus(X1, X2) -> plus(X1, X2) 1158.55/297.03 , a__plus(N, 0()) -> mark(N) 1158.55/297.03 , a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1158.55/297.03 , a__x(X1, X2) -> x(X1, X2) 1158.55/297.03 , a__x(N, 0()) -> 0() 1158.55/297.03 , a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) } 1158.55/297.03 Obligation: 1158.55/297.03 runtime complexity 1158.55/297.03 Answer: 1158.55/297.03 MAYBE 1158.55/297.03 1158.55/297.03 None of the processors succeeded. 1158.55/297.03 1158.55/297.03 Details of failed attempt(s): 1158.55/297.03 ----------------------------- 1158.55/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1158.55/297.03 following reason: 1158.55/297.03 1158.55/297.03 Computation stopped due to timeout after 297.0 seconds. 1158.55/297.03 1158.55/297.03 2) 'Best' failed due to the following reason: 1158.55/297.03 1158.55/297.03 None of the processors succeeded. 1158.55/297.03 1158.55/297.03 Details of failed attempt(s): 1158.55/297.03 ----------------------------- 1158.55/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1158.55/297.03 seconds)' failed due to the following reason: 1158.55/297.03 1158.55/297.03 Computation stopped due to timeout after 148.0 seconds. 1158.55/297.03 1158.55/297.03 2) 'Best' failed due to the following reason: 1158.55/297.03 1158.55/297.03 None of the processors succeeded. 1158.55/297.03 1158.55/297.03 Details of failed attempt(s): 1158.55/297.03 ----------------------------- 1158.55/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1158.55/297.03 following reason: 1158.55/297.03 1158.55/297.03 The processor is inapplicable, reason: 1158.55/297.03 Processor only applicable for innermost runtime complexity analysis 1158.55/297.03 1158.55/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1158.55/297.03 to the following reason: 1158.55/297.03 1158.55/297.03 The processor is inapplicable, reason: 1158.55/297.03 Processor only applicable for innermost runtime complexity analysis 1158.55/297.03 1158.55/297.03 1158.55/297.03 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1158.55/297.03 failed due to the following reason: 1158.55/297.03 1158.55/297.03 None of the processors succeeded. 1158.55/297.03 1158.55/297.03 Details of failed attempt(s): 1158.55/297.03 ----------------------------- 1158.55/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1158.55/297.03 failed due to the following reason: 1158.55/297.03 1158.55/297.03 match-boundness of the problem could not be verified. 1158.55/297.03 1158.55/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1158.55/297.03 failed due to the following reason: 1158.55/297.03 1158.55/297.03 match-boundness of the problem could not be verified. 1158.55/297.03 1158.55/297.03 1158.55/297.03 1158.55/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1158.55/297.03 the following reason: 1158.55/297.03 1158.55/297.03 We add the following weak dependency pairs: 1158.55/297.03 1158.55/297.03 Strict DPs: 1158.55/297.03 { a__and^#(X1, X2) -> c_1(X1, X2) 1158.55/297.03 , a__and^#(tt(), X) -> c_2(mark^#(X)) 1158.55/297.03 , mark^#(tt()) -> c_3() 1158.55/297.03 , mark^#(0()) -> c_4() 1158.55/297.03 , mark^#(s(X)) -> c_5(mark^#(X)) 1158.55/297.03 , mark^#(and(X1, X2)) -> c_6(a__and^#(mark(X1), X2)) 1158.55/297.03 , mark^#(plus(X1, X2)) -> c_7(a__plus^#(mark(X1), mark(X2))) 1158.55/297.03 , mark^#(x(X1, X2)) -> c_8(a__x^#(mark(X1), mark(X2))) 1158.55/297.03 , a__plus^#(X1, X2) -> c_9(X1, X2) 1158.55/297.03 , a__plus^#(N, 0()) -> c_10(mark^#(N)) 1158.55/297.03 , a__plus^#(N, s(M)) -> c_11(a__plus^#(mark(N), mark(M))) 1158.55/297.03 , a__x^#(X1, X2) -> c_12(X1, X2) 1158.55/297.03 , a__x^#(N, 0()) -> c_13() 1158.55/297.03 , a__x^#(N, s(M)) -> 1158.55/297.03 c_14(a__plus^#(a__x(mark(N), mark(M)), mark(N))) } 1158.55/297.03 1158.55/297.03 and mark the set of starting terms. 1158.55/297.03 1158.55/297.03 We are left with following problem, upon which TcT provides the 1158.55/297.03 certificate MAYBE. 1158.55/297.03 1158.55/297.03 Strict DPs: 1158.55/297.03 { a__and^#(X1, X2) -> c_1(X1, X2) 1158.55/297.03 , a__and^#(tt(), X) -> c_2(mark^#(X)) 1158.55/297.03 , mark^#(tt()) -> c_3() 1158.55/297.03 , mark^#(0()) -> c_4() 1158.55/297.03 , mark^#(s(X)) -> c_5(mark^#(X)) 1158.55/297.03 , mark^#(and(X1, X2)) -> c_6(a__and^#(mark(X1), X2)) 1158.55/297.03 , mark^#(plus(X1, X2)) -> c_7(a__plus^#(mark(X1), mark(X2))) 1158.55/297.03 , mark^#(x(X1, X2)) -> c_8(a__x^#(mark(X1), mark(X2))) 1158.55/297.03 , a__plus^#(X1, X2) -> c_9(X1, X2) 1158.55/297.03 , a__plus^#(N, 0()) -> c_10(mark^#(N)) 1158.55/297.03 , a__plus^#(N, s(M)) -> c_11(a__plus^#(mark(N), mark(M))) 1158.55/297.03 , a__x^#(X1, X2) -> c_12(X1, X2) 1158.55/297.03 , a__x^#(N, 0()) -> c_13() 1158.55/297.03 , a__x^#(N, s(M)) -> 1158.55/297.03 c_14(a__plus^#(a__x(mark(N), mark(M)), mark(N))) } 1158.55/297.03 Strict Trs: 1158.55/297.03 { a__and(X1, X2) -> and(X1, X2) 1158.55/297.03 , a__and(tt(), X) -> mark(X) 1158.55/297.03 , mark(tt()) -> tt() 1158.55/297.03 , mark(0()) -> 0() 1158.55/297.03 , mark(s(X)) -> s(mark(X)) 1158.55/297.03 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 1158.55/297.03 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1158.55/297.03 , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1158.55/297.03 , a__plus(X1, X2) -> plus(X1, X2) 1158.55/297.03 , a__plus(N, 0()) -> mark(N) 1158.55/297.03 , a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1158.55/297.03 , a__x(X1, X2) -> x(X1, X2) 1158.55/297.03 , a__x(N, 0()) -> 0() 1158.55/297.03 , a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) } 1158.55/297.03 Obligation: 1158.55/297.03 runtime complexity 1158.55/297.03 Answer: 1158.55/297.03 MAYBE 1158.55/297.03 1158.55/297.03 We estimate the number of application of {3,4,13} by applications 1158.55/297.03 of Pre({3,4,13}) = {1,2,5,8,9,10,12}. Here rules are labeled as 1158.55/297.03 follows: 1158.55/297.03 1158.55/297.03 DPs: 1158.55/297.03 { 1: a__and^#(X1, X2) -> c_1(X1, X2) 1158.55/297.03 , 2: a__and^#(tt(), X) -> c_2(mark^#(X)) 1158.55/297.03 , 3: mark^#(tt()) -> c_3() 1158.55/297.03 , 4: mark^#(0()) -> c_4() 1158.55/297.03 , 5: mark^#(s(X)) -> c_5(mark^#(X)) 1158.55/297.03 , 6: mark^#(and(X1, X2)) -> c_6(a__and^#(mark(X1), X2)) 1158.55/297.03 , 7: mark^#(plus(X1, X2)) -> c_7(a__plus^#(mark(X1), mark(X2))) 1158.55/297.03 , 8: mark^#(x(X1, X2)) -> c_8(a__x^#(mark(X1), mark(X2))) 1158.55/297.03 , 9: a__plus^#(X1, X2) -> c_9(X1, X2) 1158.55/297.03 , 10: a__plus^#(N, 0()) -> c_10(mark^#(N)) 1158.55/297.03 , 11: a__plus^#(N, s(M)) -> c_11(a__plus^#(mark(N), mark(M))) 1158.55/297.03 , 12: a__x^#(X1, X2) -> c_12(X1, X2) 1158.55/297.03 , 13: a__x^#(N, 0()) -> c_13() 1158.55/297.03 , 14: a__x^#(N, s(M)) -> 1158.55/297.03 c_14(a__plus^#(a__x(mark(N), mark(M)), mark(N))) } 1158.55/297.03 1158.55/297.03 We are left with following problem, upon which TcT provides the 1158.55/297.03 certificate MAYBE. 1158.55/297.03 1158.55/297.03 Strict DPs: 1158.55/297.03 { a__and^#(X1, X2) -> c_1(X1, X2) 1158.55/297.03 , a__and^#(tt(), X) -> c_2(mark^#(X)) 1158.55/297.03 , mark^#(s(X)) -> c_5(mark^#(X)) 1158.55/297.03 , mark^#(and(X1, X2)) -> c_6(a__and^#(mark(X1), X2)) 1158.55/297.03 , mark^#(plus(X1, X2)) -> c_7(a__plus^#(mark(X1), mark(X2))) 1158.55/297.03 , mark^#(x(X1, X2)) -> c_8(a__x^#(mark(X1), mark(X2))) 1158.55/297.03 , a__plus^#(X1, X2) -> c_9(X1, X2) 1158.55/297.03 , a__plus^#(N, 0()) -> c_10(mark^#(N)) 1158.55/297.03 , a__plus^#(N, s(M)) -> c_11(a__plus^#(mark(N), mark(M))) 1158.55/297.03 , a__x^#(X1, X2) -> c_12(X1, X2) 1158.55/297.03 , a__x^#(N, s(M)) -> 1158.55/297.03 c_14(a__plus^#(a__x(mark(N), mark(M)), mark(N))) } 1158.55/297.03 Strict Trs: 1158.55/297.03 { a__and(X1, X2) -> and(X1, X2) 1158.55/297.03 , a__and(tt(), X) -> mark(X) 1158.55/297.03 , mark(tt()) -> tt() 1158.55/297.03 , mark(0()) -> 0() 1158.55/297.03 , mark(s(X)) -> s(mark(X)) 1158.55/297.03 , mark(and(X1, X2)) -> a__and(mark(X1), X2) 1158.55/297.03 , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) 1158.55/297.03 , mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) 1158.55/297.03 , a__plus(X1, X2) -> plus(X1, X2) 1158.55/297.03 , a__plus(N, 0()) -> mark(N) 1158.55/297.03 , a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) 1158.55/297.03 , a__x(X1, X2) -> x(X1, X2) 1158.55/297.03 , a__x(N, 0()) -> 0() 1158.55/297.03 , a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) } 1158.55/297.03 Weak DPs: 1158.55/297.03 { mark^#(tt()) -> c_3() 1158.55/297.03 , mark^#(0()) -> c_4() 1158.55/297.03 , a__x^#(N, 0()) -> c_13() } 1158.55/297.03 Obligation: 1158.55/297.03 runtime complexity 1158.55/297.03 Answer: 1158.55/297.03 MAYBE 1158.55/297.03 1158.55/297.03 Empty strict component of the problem is NOT empty. 1158.55/297.03 1158.55/297.03 1158.55/297.03 Arrrr.. 1159.21/297.62 EOF