MAYBE 1159.37/297.02 MAYBE 1159.37/297.02 1159.37/297.02 We are left with following problem, upon which TcT provides the 1159.37/297.02 certificate MAYBE. 1159.37/297.02 1159.37/297.02 Strict Trs: 1159.37/297.02 { -(x, 0()) -> x 1159.37/297.02 , -(s(x), s(y)) -> -(x, y) 1159.37/297.02 , +(0(), y) -> y 1159.37/297.02 , +(s(x), y) -> s(+(x, y)) 1159.37/297.02 , *(x, 0()) -> 0() 1159.37/297.02 , *(x, s(y)) -> +(x, *(x, y)) 1159.37/297.02 , f(s(x)) -> 1159.37/297.02 f(-(+(*(s(x), s(x)), *(s(x), s(s(s(0()))))), 1159.37/297.02 *(s(s(x)), s(s(x))))) } 1159.37/297.02 Obligation: 1159.37/297.02 runtime complexity 1159.37/297.02 Answer: 1159.37/297.02 MAYBE 1159.37/297.02 1159.37/297.02 None of the processors succeeded. 1159.37/297.02 1159.37/297.02 Details of failed attempt(s): 1159.37/297.02 ----------------------------- 1159.37/297.02 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 1159.37/297.02 following reason: 1159.37/297.02 1159.37/297.02 Computation stopped due to timeout after 297.0 seconds. 1159.37/297.02 1159.37/297.02 2) 'Best' failed due to the following reason: 1159.37/297.02 1159.37/297.02 None of the processors succeeded. 1159.37/297.02 1159.37/297.02 Details of failed attempt(s): 1159.37/297.02 ----------------------------- 1159.37/297.02 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 1159.37/297.02 seconds)' failed due to the following reason: 1159.37/297.02 1159.37/297.02 Computation stopped due to timeout after 148.0 seconds. 1159.37/297.02 1159.37/297.02 2) 'Best' failed due to the following reason: 1159.37/297.02 1159.37/297.02 None of the processors succeeded. 1159.37/297.02 1159.37/297.02 Details of failed attempt(s): 1159.37/297.02 ----------------------------- 1159.37/297.02 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 1159.37/297.02 to the following reason: 1159.37/297.02 1159.37/297.02 The processor is inapplicable, reason: 1159.37/297.02 Processor only applicable for innermost runtime complexity analysis 1159.37/297.02 1159.37/297.02 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 1159.37/297.02 following reason: 1159.37/297.02 1159.37/297.02 The processor is inapplicable, reason: 1159.37/297.02 Processor only applicable for innermost runtime complexity analysis 1159.37/297.02 1159.37/297.02 1159.37/297.02 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 1159.37/297.02 failed due to the following reason: 1159.37/297.02 1159.37/297.02 None of the processors succeeded. 1159.37/297.02 1159.37/297.02 Details of failed attempt(s): 1159.37/297.02 ----------------------------- 1159.37/297.02 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 1159.37/297.02 failed due to the following reason: 1159.37/297.02 1159.37/297.02 match-boundness of the problem could not be verified. 1159.37/297.02 1159.37/297.02 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 1159.37/297.02 failed due to the following reason: 1159.37/297.02 1159.37/297.02 match-boundness of the problem could not be verified. 1159.37/297.02 1159.37/297.02 1159.37/297.02 1159.37/297.02 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 1159.37/297.02 the following reason: 1159.37/297.02 1159.37/297.02 We add the following weak dependency pairs: 1159.37/297.02 1159.37/297.02 Strict DPs: 1159.37/297.02 { -^#(x, 0()) -> c_1(x) 1159.37/297.02 , -^#(s(x), s(y)) -> c_2(-^#(x, y)) 1159.37/297.02 , +^#(0(), y) -> c_3(y) 1159.37/297.02 , +^#(s(x), y) -> c_4(+^#(x, y)) 1159.37/297.02 , *^#(x, 0()) -> c_5() 1159.37/297.02 , *^#(x, s(y)) -> c_6(+^#(x, *(x, y))) 1159.37/297.02 , f^#(s(x)) -> 1159.37/297.02 c_7(f^#(-(+(*(s(x), s(x)), *(s(x), s(s(s(0()))))), 1159.37/297.02 *(s(s(x)), s(s(x)))))) } 1159.37/297.02 1159.37/297.02 and mark the set of starting terms. 1159.37/297.02 1159.37/297.02 We are left with following problem, upon which TcT provides the 1159.37/297.02 certificate MAYBE. 1159.37/297.02 1159.37/297.02 Strict DPs: 1159.37/297.02 { -^#(x, 0()) -> c_1(x) 1159.37/297.02 , -^#(s(x), s(y)) -> c_2(-^#(x, y)) 1159.37/297.02 , +^#(0(), y) -> c_3(y) 1159.37/297.02 , +^#(s(x), y) -> c_4(+^#(x, y)) 1159.37/297.02 , *^#(x, 0()) -> c_5() 1159.37/297.02 , *^#(x, s(y)) -> c_6(+^#(x, *(x, y))) 1159.37/297.02 , f^#(s(x)) -> 1159.37/297.02 c_7(f^#(-(+(*(s(x), s(x)), *(s(x), s(s(s(0()))))), 1159.37/297.02 *(s(s(x)), s(s(x)))))) } 1159.37/297.02 Strict Trs: 1159.37/297.02 { -(x, 0()) -> x 1159.37/297.02 , -(s(x), s(y)) -> -(x, y) 1159.37/297.02 , +(0(), y) -> y 1159.37/297.02 , +(s(x), y) -> s(+(x, y)) 1159.37/297.02 , *(x, 0()) -> 0() 1159.37/297.02 , *(x, s(y)) -> +(x, *(x, y)) 1159.37/297.02 , f(s(x)) -> 1159.37/297.02 f(-(+(*(s(x), s(x)), *(s(x), s(s(s(0()))))), 1159.37/297.02 *(s(s(x)), s(s(x))))) } 1159.37/297.02 Obligation: 1159.37/297.02 runtime complexity 1159.37/297.02 Answer: 1159.37/297.02 MAYBE 1159.37/297.02 1159.37/297.02 We estimate the number of application of {5} by applications of 1159.37/297.02 Pre({5}) = {1,3}. Here rules are labeled as follows: 1159.37/297.02 1159.37/297.02 DPs: 1159.37/297.02 { 1: -^#(x, 0()) -> c_1(x) 1159.37/297.02 , 2: -^#(s(x), s(y)) -> c_2(-^#(x, y)) 1159.37/297.02 , 3: +^#(0(), y) -> c_3(y) 1159.37/297.02 , 4: +^#(s(x), y) -> c_4(+^#(x, y)) 1159.37/297.02 , 5: *^#(x, 0()) -> c_5() 1159.37/297.02 , 6: *^#(x, s(y)) -> c_6(+^#(x, *(x, y))) 1159.37/297.02 , 7: f^#(s(x)) -> 1159.37/297.02 c_7(f^#(-(+(*(s(x), s(x)), *(s(x), s(s(s(0()))))), 1159.37/297.02 *(s(s(x)), s(s(x)))))) } 1159.37/297.02 1159.37/297.02 We are left with following problem, upon which TcT provides the 1159.37/297.02 certificate MAYBE. 1159.37/297.02 1159.37/297.02 Strict DPs: 1159.37/297.02 { -^#(x, 0()) -> c_1(x) 1159.37/297.02 , -^#(s(x), s(y)) -> c_2(-^#(x, y)) 1159.37/297.02 , +^#(0(), y) -> c_3(y) 1159.37/297.02 , +^#(s(x), y) -> c_4(+^#(x, y)) 1159.37/297.02 , *^#(x, s(y)) -> c_6(+^#(x, *(x, y))) 1159.37/297.02 , f^#(s(x)) -> 1159.37/297.02 c_7(f^#(-(+(*(s(x), s(x)), *(s(x), s(s(s(0()))))), 1159.37/297.02 *(s(s(x)), s(s(x)))))) } 1159.37/297.02 Strict Trs: 1159.37/297.02 { -(x, 0()) -> x 1159.37/297.02 , -(s(x), s(y)) -> -(x, y) 1159.37/297.02 , +(0(), y) -> y 1159.37/297.02 , +(s(x), y) -> s(+(x, y)) 1159.37/297.02 , *(x, 0()) -> 0() 1159.37/297.02 , *(x, s(y)) -> +(x, *(x, y)) 1159.37/297.02 , f(s(x)) -> 1159.37/297.02 f(-(+(*(s(x), s(x)), *(s(x), s(s(s(0()))))), 1159.37/297.02 *(s(s(x)), s(s(x))))) } 1159.37/297.02 Weak DPs: { *^#(x, 0()) -> c_5() } 1159.37/297.02 Obligation: 1159.37/297.02 runtime complexity 1159.37/297.02 Answer: 1159.37/297.02 MAYBE 1159.37/297.02 1159.37/297.02 Empty strict component of the problem is NOT empty. 1159.37/297.02 1159.37/297.02 1159.37/297.02 Arrrr.. 1160.01/297.62 EOF