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TRS Stand 20472 pair #381711933
details
property
value
status
complete
benchmark
09.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n027.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.68854999542 seconds
cpu usage
4.014875459
max memory
2.41967104E8
stage attributes
key
value
output-size
2888
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 58 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 12 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, y, w, w, a) -> g1(x, x, y, w) f(x, y, w, a, a) -> g1(y, x, x, w) f(x, y, a, a, w) -> g2(x, y, y, w) f(x, y, a, w, w) -> g2(y, y, x, w) g1(x, x, y, a) -> h(x, y) g1(y, x, x, a) -> h(x, y) g2(x, y, y, a) -> h(x, y) g2(y, y, x, a) -> h(x, y) h(x, x) -> x Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(f(x_1, x_2, x_3, x_4, x_5)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 + x_4 + 2*x_5 POL(g1(x_1, x_2, x_3, x_4)) = 2 + x_1 + x_2 + x_3 + 2*x_4 POL(g2(x_1, x_2, x_3, x_4)) = 2 + x_1 + x_2 + x_3 + 2*x_4 POL(h(x_1, x_2)) = 1 + x_1 + x_2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g1(x, x, y, a) -> h(x, y) g1(y, x, x, a) -> h(x, y) g2(x, y, y, a) -> h(x, y) g2(y, y, x, a) -> h(x, y) h(x, x) -> x ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, y, w, w, a) -> g1(x, x, y, w) f(x, y, w, a, a) -> g1(y, x, x, w) f(x, y, a, a, w) -> g2(x, y, y, w) f(x, y, a, w, w) -> g2(y, y, x, w) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 2 POL(f(x_1, x_2, x_3, x_4, x_5)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 + 2*x_4 + 2*x_5 POL(g1(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + 2*x_4 POL(g2(x_1, x_2, x_3, x_4)) = 1 + x_1 + x_2 + x_3 + 2*x_4 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(x, y, w, w, a) -> g1(x, x, y, w) f(x, y, w, a, a) -> g1(y, x, x, w) f(x, y, a, a, w) -> g2(x, y, y, w) f(x, y, a, w, w) -> g2(y, y, x, w) ---------------------------------------- (4)
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