details

property	value
status	complete
benchmark	gen-25.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	Secret_06_TRS

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	14.5725231171 seconds
cpu usage	34.812305964
max memory	1.536036864E9

stage attributes

key	value
output-size	5105
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 857 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a, f(b(b(z, y), a))) -> z c(c(z, x, a), a, y) -> f(f(c(y, a, f(c(z, y, x))))) f(f(c(a, y, z))) -> b(y, b(z, z)) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: C(c(z, x, a), a, y) -> F(f(c(y, a, f(c(z, y, x))))) C(c(z, x, a), a, y) -> F(c(y, a, f(c(z, y, x)))) C(c(z, x, a), a, y) -> C(y, a, f(c(z, y, x))) C(c(z, x, a), a, y) -> F(c(z, y, x)) C(c(z, x, a), a, y) -> C(z, y, x) F(f(c(a, y, z))) -> B(y, b(z, z)) F(f(c(a, y, z))) -> B(z, z) The TRS R consists of the following rules: b(a, f(b(b(z, y), a))) -> z c(c(z, x, a), a, y) -> f(f(c(y, a, f(c(z, y, x))))) f(f(c(a, y, z))) -> b(y, b(z, z)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: C(c(z, x, a), a, y) -> C(z, y, x) C(c(z, x, a), a, y) -> C(y, a, f(c(z, y, x))) The TRS R consists of the following rules: b(a, f(b(b(z, y), a))) -> z c(c(z, x, a), a, y) -> f(f(c(y, a, f(c(z, y, x))))) f(f(c(a, y, z))) -> b(y, b(z, z)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. C(c(z, x, a), a, y) -> C(y, a, f(c(z, y, x))) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Standard