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TRS Stand 20472 pair #381714312
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
n095.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.79591608047 seconds
cpu usage
7.776351311
max memory
5.09124608E8
stage attributes
key
value
output-size
30244
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES (15) QDP (16) UsableRulesProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPOrderProof [EQUIVALENT, 77 ms] (22) QDP (23) QDPOrderProof [EQUIVALENT, 32 ms] (24) QDP (25) QDPSizeChangeProof [EQUIVALENT, 0 ms] (26) YES (27) QDP (28) QDPOrderProof [EQUIVALENT, 26 ms] (29) QDP (30) PisEmptyProof [EQUIVALENT, 0 ms] (31) YES (32) QDP (33) UsableRulesProof [EQUIVALENT, 0 ms] (34) QDP (35) QDPSizeChangeProof [EQUIVALENT, 0 ms] (36) YES (37) QDP (38) UsableRulesProof [EQUIVALENT, 0 ms] (39) QDP (40) QDPSizeChangeProof [EQUIVALENT, 0 ms] (41) YES (42) QDP (43) QDPOrderProof [EQUIVALENT, 47 ms] (44) QDP (45) PisEmptyProof [EQUIVALENT, 0 ms] (46) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: 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) Q is empty.
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