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TRS Standard pair #516964750
details
property
value
status
complete
benchmark
test829.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n065.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.11599993706 seconds
cpu usage
5.66536984
max memory
4.70183936E8
stage attributes
key
value
output-size
2053
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 75 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5)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(c(X, s(Y))) -> f(c(s(X), Y)) g(c(s(X), Y)) -> f(c(X, s(Y))) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(c(x_1, x_2)) = x_1 + 2*x_2 POL(f(x_1)) = 2*x_1 POL(g(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: g(c(s(X), Y)) -> f(c(X, s(Y))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(c(X, s(Y))) -> f(c(s(X), Y)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(c(x_1, x_2)) = x_1 + 2*x_2 POL(f(x_1)) = 2*x_1 POL(s(x_1)) = 2 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(c(X, s(Y))) -> f(c(s(X), Y)) ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (6) YES
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