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Derivational Complexity: TRS Innermost pair #487105244
details
property
value
status
complete
benchmark
wiehe12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.918 seconds
cpu usage
1039.89
user time
1032.05
system time
7.84201
max virtual memory
1.9829924E7
max residence set size
1.4888816E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^2, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 619 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 293 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 84 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 79 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 76 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 1303 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^2, INF) (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 0 ms] (30) typed CpxTrs ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: g(s(x), s(y)) -> if(and(f(s(x)), f(s(y))), t(g(k(minus(m(x, y), n(x, y)), s(s(0))), k(n(s(x), s(y)), s(s(0))))), g(minus(m(x, y), n(x, y)), n(s(x), s(y)))) n(0, y) -> 0 n(x, 0) -> 0 n(s(x), s(y)) -> s(n(x, y)) m(0, y) -> y m(x, 0) -> x m(s(x), s(y)) -> s(m(x, y)) k(0, s(y)) -> 0 k(s(x), s(y)) -> s(k(minus(x, y), s(y))) t(x) -> p(x, x) p(s(x), s(y)) -> s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))) p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x)) p(0, y) -> y p(id(x), s(y)) -> s(p(x, if(gt(s(y), y), y, s(y)))) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) id(x) -> x if(true, x, y) -> x if(false, x, y) -> y not(x) -> if(x, false, true) and(x, false) -> false and(true, true) -> true f(0) -> true f(s(x)) -> h(x) h(0) -> false h(s(x)) -> f(x) gt(s(x), 0) -> true gt(0, y) -> false gt(s(x), s(y)) -> gt(x, y) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(true) -> true encArg(false) -> false encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(cons_n(x_1, x_2)) -> n(encArg(x_1), encArg(x_2)) encArg(cons_m(x_1, x_2)) -> m(encArg(x_1), encArg(x_2)) encArg(cons_k(x_1, x_2)) -> k(encArg(x_1), encArg(x_2)) encArg(cons_t(x_1)) -> t(encArg(x_1)) encArg(cons_p(x_1, x_2)) -> p(encArg(x_1), encArg(x_2)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_id(x_1)) -> id(encArg(x_1)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_not(x_1)) -> not(encArg(x_1))
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