MAYBE 770.25/297.03 MAYBE 770.25/297.03 770.25/297.03 We are left with following problem, upon which TcT provides the 770.25/297.03 certificate MAYBE. 770.25/297.03 770.25/297.03 Strict Trs: 770.25/297.03 { eq(0(), 0()) -> true() 770.25/297.03 , eq(0(), s(x)) -> false() 770.25/297.03 , eq(s(x), 0()) -> false() 770.25/297.03 , eq(s(x), s(y)) -> eq(x, y) 770.25/297.03 , or(true(), y) -> true() 770.25/297.03 , or(false(), y) -> y 770.25/297.03 , union(empty(), h) -> h 770.25/297.03 , union(edge(x, y, i), h) -> edge(x, y, union(i, h)) 770.25/297.03 , reach(x, y, empty(), h) -> false() 770.25/297.03 , reach(x, y, edge(u, v, i), h) -> 770.25/297.03 if_reach_1(eq(x, u), x, y, edge(u, v, i), h) 770.25/297.03 , if_reach_1(true(), x, y, edge(u, v, i), h) -> 770.25/297.03 if_reach_2(eq(y, v), x, y, edge(u, v, i), h) 770.25/297.03 , if_reach_1(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 reach(x, y, i, edge(u, v, h)) 770.25/297.03 , if_reach_2(true(), x, y, edge(u, v, i), h) -> true() 770.25/297.03 , if_reach_2(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 or(reach(x, y, i, h), reach(v, y, union(i, h), empty())) } 770.25/297.03 Obligation: 770.25/297.03 runtime complexity 770.25/297.03 Answer: 770.25/297.03 MAYBE 770.25/297.03 770.25/297.03 None of the processors succeeded. 770.25/297.03 770.25/297.03 Details of failed attempt(s): 770.25/297.03 ----------------------------- 770.25/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 770.25/297.03 following reason: 770.25/297.03 770.25/297.03 Computation stopped due to timeout after 297.0 seconds. 770.25/297.03 770.25/297.03 2) 'Best' failed due to the following reason: 770.25/297.03 770.25/297.03 None of the processors succeeded. 770.25/297.03 770.25/297.03 Details of failed attempt(s): 770.25/297.03 ----------------------------- 770.25/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 770.25/297.03 seconds)' failed due to the following reason: 770.25/297.03 770.25/297.03 Computation stopped due to timeout after 148.0 seconds. 770.25/297.03 770.25/297.03 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 770.25/297.03 failed due to the following reason: 770.25/297.03 770.25/297.03 None of the processors succeeded. 770.25/297.03 770.25/297.03 Details of failed attempt(s): 770.25/297.03 ----------------------------- 770.25/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 770.25/297.03 failed due to the following reason: 770.25/297.03 770.25/297.03 match-boundness of the problem could not be verified. 770.25/297.03 770.25/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 770.25/297.03 failed due to the following reason: 770.25/297.03 770.25/297.03 match-boundness of the problem could not be verified. 770.25/297.03 770.25/297.03 770.25/297.03 3) 'Best' failed due to the following reason: 770.25/297.03 770.25/297.03 None of the processors succeeded. 770.25/297.03 770.25/297.03 Details of failed attempt(s): 770.25/297.03 ----------------------------- 770.25/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 770.25/297.03 following reason: 770.25/297.03 770.25/297.03 The processor is inapplicable, reason: 770.25/297.03 Processor only applicable for innermost runtime complexity analysis 770.25/297.03 770.25/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 770.25/297.03 to the following reason: 770.25/297.03 770.25/297.03 The processor is inapplicable, reason: 770.25/297.03 Processor only applicable for innermost runtime complexity analysis 770.25/297.03 770.25/297.03 770.25/297.03 770.25/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 770.25/297.03 the following reason: 770.25/297.03 770.25/297.03 We add the following weak dependency pairs: 770.25/297.03 770.25/297.03 Strict DPs: 770.25/297.03 { eq^#(0(), 0()) -> c_1() 770.25/297.03 , eq^#(0(), s(x)) -> c_2() 770.25/297.03 , eq^#(s(x), 0()) -> c_3() 770.25/297.03 , eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 770.25/297.03 , or^#(true(), y) -> c_5() 770.25/297.03 , or^#(false(), y) -> c_6(y) 770.25/297.03 , union^#(empty(), h) -> c_7(h) 770.25/297.03 , union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h)) 770.25/297.03 , reach^#(x, y, empty(), h) -> c_9() 770.25/297.03 , reach^#(x, y, edge(u, v, i), h) -> 770.25/297.03 c_10(if_reach_1^#(eq(x, u), x, y, edge(u, v, i), h)) 770.25/297.03 , if_reach_1^#(true(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_11(if_reach_2^#(eq(y, v), x, y, edge(u, v, i), h)) 770.25/297.03 , if_reach_1^#(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_12(reach^#(x, y, i, edge(u, v, h))) 770.25/297.03 , if_reach_2^#(true(), x, y, edge(u, v, i), h) -> c_13() 770.25/297.03 , if_reach_2^#(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_14(or^#(reach(x, y, i, h), reach(v, y, union(i, h), empty()))) } 770.25/297.03 770.25/297.03 and mark the set of starting terms. 770.25/297.03 770.25/297.03 We are left with following problem, upon which TcT provides the 770.25/297.03 certificate MAYBE. 770.25/297.03 770.25/297.03 Strict DPs: 770.25/297.03 { eq^#(0(), 0()) -> c_1() 770.25/297.03 , eq^#(0(), s(x)) -> c_2() 770.25/297.03 , eq^#(s(x), 0()) -> c_3() 770.25/297.03 , eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 770.25/297.03 , or^#(true(), y) -> c_5() 770.25/297.03 , or^#(false(), y) -> c_6(y) 770.25/297.03 , union^#(empty(), h) -> c_7(h) 770.25/297.03 , union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h)) 770.25/297.03 , reach^#(x, y, empty(), h) -> c_9() 770.25/297.03 , reach^#(x, y, edge(u, v, i), h) -> 770.25/297.03 c_10(if_reach_1^#(eq(x, u), x, y, edge(u, v, i), h)) 770.25/297.03 , if_reach_1^#(true(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_11(if_reach_2^#(eq(y, v), x, y, edge(u, v, i), h)) 770.25/297.03 , if_reach_1^#(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_12(reach^#(x, y, i, edge(u, v, h))) 770.25/297.03 , if_reach_2^#(true(), x, y, edge(u, v, i), h) -> c_13() 770.25/297.03 , if_reach_2^#(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_14(or^#(reach(x, y, i, h), reach(v, y, union(i, h), empty()))) } 770.25/297.03 Strict Trs: 770.25/297.03 { eq(0(), 0()) -> true() 770.25/297.03 , eq(0(), s(x)) -> false() 770.25/297.03 , eq(s(x), 0()) -> false() 770.25/297.03 , eq(s(x), s(y)) -> eq(x, y) 770.25/297.03 , or(true(), y) -> true() 770.25/297.03 , or(false(), y) -> y 770.25/297.03 , union(empty(), h) -> h 770.25/297.03 , union(edge(x, y, i), h) -> edge(x, y, union(i, h)) 770.25/297.03 , reach(x, y, empty(), h) -> false() 770.25/297.03 , reach(x, y, edge(u, v, i), h) -> 770.25/297.03 if_reach_1(eq(x, u), x, y, edge(u, v, i), h) 770.25/297.03 , if_reach_1(true(), x, y, edge(u, v, i), h) -> 770.25/297.03 if_reach_2(eq(y, v), x, y, edge(u, v, i), h) 770.25/297.03 , if_reach_1(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 reach(x, y, i, edge(u, v, h)) 770.25/297.03 , if_reach_2(true(), x, y, edge(u, v, i), h) -> true() 770.25/297.03 , if_reach_2(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 or(reach(x, y, i, h), reach(v, y, union(i, h), empty())) } 770.25/297.03 Obligation: 770.25/297.03 runtime complexity 770.25/297.03 Answer: 770.25/297.03 MAYBE 770.25/297.03 770.25/297.03 We estimate the number of application of {1,2,3,5,9,13} by 770.25/297.03 applications of Pre({1,2,3,5,9,13}) = {4,6,7,8,11,12,14}. Here 770.25/297.03 rules are labeled as follows: 770.25/297.03 770.25/297.03 DPs: 770.25/297.03 { 1: eq^#(0(), 0()) -> c_1() 770.25/297.03 , 2: eq^#(0(), s(x)) -> c_2() 770.25/297.03 , 3: eq^#(s(x), 0()) -> c_3() 770.25/297.03 , 4: eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 770.25/297.03 , 5: or^#(true(), y) -> c_5() 770.25/297.03 , 6: or^#(false(), y) -> c_6(y) 770.25/297.03 , 7: union^#(empty(), h) -> c_7(h) 770.25/297.03 , 8: union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h)) 770.25/297.03 , 9: reach^#(x, y, empty(), h) -> c_9() 770.25/297.03 , 10: reach^#(x, y, edge(u, v, i), h) -> 770.25/297.03 c_10(if_reach_1^#(eq(x, u), x, y, edge(u, v, i), h)) 770.25/297.03 , 11: if_reach_1^#(true(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_11(if_reach_2^#(eq(y, v), x, y, edge(u, v, i), h)) 770.25/297.03 , 12: if_reach_1^#(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_12(reach^#(x, y, i, edge(u, v, h))) 770.25/297.03 , 13: if_reach_2^#(true(), x, y, edge(u, v, i), h) -> c_13() 770.25/297.03 , 14: if_reach_2^#(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_14(or^#(reach(x, y, i, h), reach(v, y, union(i, h), empty()))) } 770.25/297.03 770.25/297.03 We are left with following problem, upon which TcT provides the 770.25/297.03 certificate MAYBE. 770.25/297.03 770.25/297.03 Strict DPs: 770.25/297.03 { eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 770.25/297.03 , or^#(false(), y) -> c_6(y) 770.25/297.03 , union^#(empty(), h) -> c_7(h) 770.25/297.03 , union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h)) 770.25/297.03 , reach^#(x, y, edge(u, v, i), h) -> 770.25/297.03 c_10(if_reach_1^#(eq(x, u), x, y, edge(u, v, i), h)) 770.25/297.03 , if_reach_1^#(true(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_11(if_reach_2^#(eq(y, v), x, y, edge(u, v, i), h)) 770.25/297.03 , if_reach_1^#(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_12(reach^#(x, y, i, edge(u, v, h))) 770.25/297.03 , if_reach_2^#(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 c_14(or^#(reach(x, y, i, h), reach(v, y, union(i, h), empty()))) } 770.25/297.03 Strict Trs: 770.25/297.03 { eq(0(), 0()) -> true() 770.25/297.03 , eq(0(), s(x)) -> false() 770.25/297.03 , eq(s(x), 0()) -> false() 770.25/297.03 , eq(s(x), s(y)) -> eq(x, y) 770.25/297.03 , or(true(), y) -> true() 770.25/297.03 , or(false(), y) -> y 770.25/297.03 , union(empty(), h) -> h 770.25/297.03 , union(edge(x, y, i), h) -> edge(x, y, union(i, h)) 770.25/297.03 , reach(x, y, empty(), h) -> false() 770.25/297.03 , reach(x, y, edge(u, v, i), h) -> 770.25/297.03 if_reach_1(eq(x, u), x, y, edge(u, v, i), h) 770.25/297.03 , if_reach_1(true(), x, y, edge(u, v, i), h) -> 770.25/297.03 if_reach_2(eq(y, v), x, y, edge(u, v, i), h) 770.25/297.03 , if_reach_1(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 reach(x, y, i, edge(u, v, h)) 770.25/297.03 , if_reach_2(true(), x, y, edge(u, v, i), h) -> true() 770.25/297.03 , if_reach_2(false(), x, y, edge(u, v, i), h) -> 770.25/297.03 or(reach(x, y, i, h), reach(v, y, union(i, h), empty())) } 770.25/297.03 Weak DPs: 770.25/297.03 { eq^#(0(), 0()) -> c_1() 770.25/297.03 , eq^#(0(), s(x)) -> c_2() 770.25/297.03 , eq^#(s(x), 0()) -> c_3() 770.25/297.03 , or^#(true(), y) -> c_5() 770.25/297.03 , reach^#(x, y, empty(), h) -> c_9() 770.25/297.03 , if_reach_2^#(true(), x, y, edge(u, v, i), h) -> c_13() } 770.25/297.03 Obligation: 770.25/297.03 runtime complexity 770.25/297.03 Answer: 770.25/297.03 MAYBE 770.25/297.03 770.25/297.03 Empty strict component of the problem is NOT empty. 770.25/297.03 770.25/297.03 770.25/297.03 Arrrr.. 770.46/297.25 EOF