details

property	value
status	complete
benchmark	gen-14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n153.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	2.07131385803 seconds
cpu usage	5.517620162
max memory	2.93441536E8

stage attributes

key	value
output-size	4075
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0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, 12 ms] (6) QDP (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(f(b(x, z)), y) -> f(f(f(b(z, b(y, z))))) c(f(f(c(x, a, z))), a, y) -> b(y, f(b(a, z))) b(b(c(b(a, a), a, z), f(a)), y) -> 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: B(f(b(x, z)), y) -> B(z, b(y, z)) B(f(b(x, z)), y) -> B(y, z) C(f(f(c(x, a, z))), a, y) -> B(y, f(b(a, z))) C(f(f(c(x, a, z))), a, y) -> B(a, z) The TRS R consists of the following rules: b(f(b(x, z)), y) -> f(f(f(b(z, b(y, z))))) c(f(f(c(x, a, z))), a, y) -> b(y, f(b(a, z))) b(b(c(b(a, a), a, z), f(a)), y) -> 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 2 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: B(f(b(x, z)), y) -> B(y, z) B(f(b(x, z)), y) -> B(z, b(y, z)) The TRS R consists of the following rules: b(f(b(x, z)), y) -> f(f(f(b(z, b(y, z))))) c(f(f(c(x, a, z))), a, y) -> b(y, f(b(a, z))) b(b(c(b(a, a), a, z), f(a)), y) -> 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. B(f(b(x, z)), y) -> B(y, z) The remaining pairs can at least be oriented weakly. Used ordering: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(B(x_1, x_2)) = [[1]] + [[0, 1]] * x_1 + [[0, 1]] * x_2 >>> <<< popout

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

job log

popout

actions

all output return to TRS Standard