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TRS Standard pair #487066753
details
property
value
status
complete
benchmark
06.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.71979 seconds
cpu usage
3.99382
user time
3.81924
system time
0.174583
max virtual memory
1.8408912E7
max residence set size
249476.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 47 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 13 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, y) -> g1(x, x, y) f(x, y) -> g1(y, x, x) f(x, y) -> g2(x, y, y) f(x, y) -> g2(y, y, x) g1(x, x, y) -> h(x, y) g1(y, x, x) -> h(x, y) g2(x, y, y) -> h(x, y) g2(y, y, x) -> h(x, y) h(x, x) -> x Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(f(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 POL(g1(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(g2(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 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: h(x, x) -> x ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, y) -> g1(x, x, y) f(x, y) -> g1(y, x, x) f(x, y) -> g2(x, y, y) f(x, y) -> g2(y, y, x) g1(x, x, y) -> h(x, y) g1(y, x, x) -> h(x, y) g2(x, y, y) -> h(x, y) g2(y, y, x) -> h(x, y) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(f(x_1, x_2)) = 2 + 2*x_1 + 2*x_2 POL(g1(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 POL(g2(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3 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: f(x, y) -> g1(x, x, y) f(x, y) -> g1(y, x, x) f(x, y) -> g2(x, y, y) f(x, y) -> g2(y, y, x) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g1(x, x, y) -> h(x, y)
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