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TRS Stand 20472 pair #381710635
details
property
value
status
complete
benchmark
identity.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.26227903366 seconds
cpu usage
5.539268054
max memory
3.71142656E8
stage attributes
key
value
output-size
13204
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 57 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 15 ms] (4) QTRS (5) AAECC Innermost [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) AND (11) QDP (12) UsableRulesProof [EQUIVALENT, 0 ms] (13) QDP (14) QReductionProof [EQUIVALENT, 0 ms] (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) QReductionProof [EQUIVALENT, 0 ms] (29) QDP (30) QDPOrderProof [EQUIVALENT, 55 ms] (31) QDP (32) PisEmptyProof [EQUIVALENT, 0 ms] (33) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(x, 0) -> 0 g(d, s(x)) -> s(s(g(d, x))) g(h, s(0)) -> 0 g(h, s(s(x))) -> s(g(h, x)) double(x) -> g(d, x) half(x) -> g(h, x) f(s(x), y) -> f(half(s(x)), double(y)) f(s(0), y) -> y id(x) -> f(x, s(0)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(d) = 0 POL(double(x_1)) = x_1 POL(f(x_1, x_2)) = 2*x_1 + 2*x_2 POL(g(x_1, x_2)) = x_1 + x_2 POL(h) = 0 POL(half(x_1)) = x_1 POL(id(x_1)) = 2 + 2*x_1 POL(s(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: id(x) -> f(x, s(0)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(x, 0) -> 0 g(d, s(x)) -> s(s(g(d, x))) g(h, s(0)) -> 0
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