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TRS Standard pair #516966305
details
property
value
status
complete
benchmark
nrvsq.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
MNZ_10
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
32.0925030708 seconds
cpu usage
89.551330141
max memory
3.24798464E9
stage attributes
key
value
output-size
28754
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 25 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) TransformationProof [EQUIVALENT, 13 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) AND (9) QDP (10) TransformationProof [EQUIVALENT, 0 ms] (11) QDP (12) DependencyGraphProof [EQUIVALENT, 0 ms] (13) QDP (14) TransformationProof [EQUIVALENT, 0 ms] (15) QDP (16) DependencyGraphProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPOrderProof [EQUIVALENT, 189 ms] (22) QDP (23) QDPOrderProof [EQUIVALENT, 85 ms] (24) QDP (25) DependencyGraphProof [EQUIVALENT, 0 ms] (26) AND (27) QDP (28) QDPOrderProof [EQUIVALENT, 7696 ms] (29) QDP (30) DependencyGraphProof [EQUIVALENT, 0 ms] (31) QDP (32) UsableRulesProof [EQUIVALENT, 0 ms] (33) QDP (34) QDPSizeChangeProof [EQUIVALENT, 0 ms] (35) YES (36) QDP (37) UsableRulesProof [EQUIVALENT, 0 ms] (38) QDP (39) QDPSizeChangeProof [EQUIVALENT, 0 ms] (40) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(g(x)) -> g(g(f(x))) g(s(x)) -> s(s(g(x))) s(x) -> h(0, x) s(x) -> h(x, 0) f(0) -> 0 s(s(s(0))) -> f(s(0)) f(s(0)) -> s(0) h(f(x), g(x)) -> f(s(x)) g(x) -> h(h(h(h(x, x), x), x), x) f(s(s(x))) -> h(f(x), g(h(x, x))) s(0) -> r(0) s(s(s(0))) -> r(s(0)) r(s(0)) -> s(0) g(x) -> r(x) s(0) -> p(0) s(s(0)) -> p(s(0)) p(s(0)) -> 0 s(s(s(s(s(0))))) -> p(s(s(0))) p(s(s(0))) -> s(s(s(0))) h(p(x), g(x)) -> p(s(x)) s(0) -> k(0) s(s(p(p(a)))) -> s(k(p(a))) s(k(p(a))) -> p(p(a)) g(x) -> k(x) a -> 0 s(h(r(k(p(x))), r(x))) -> h(r(r(p(x))), k(x)) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation:
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