details

property	value
status	complete
benchmark	jwttt.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n076.star.cs.uiowa.edu
space	Waldmann_06

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.00414919853 seconds
cpu usage	7.253650983
max memory	5.13478656E8

stage attributes

key	value
output-size	5841
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 15 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 39 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 9 ms] (12) QDP (13) PisEmptyProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, f(a, y)) -> f(a, f(f(a, h(f(a, x))), y)) 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: F(x, f(a, y)) -> F(a, f(f(a, h(f(a, x))), y)) F(x, f(a, y)) -> F(f(a, h(f(a, x))), y) F(x, f(a, y)) -> F(a, h(f(a, x))) F(x, f(a, y)) -> F(a, x) The TRS R consists of the following rules: f(x, f(a, y)) -> f(a, f(f(a, h(f(a, x))), y)) 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 1 less node. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(x, f(a, y)) -> F(f(a, h(f(a, x))), y) F(x, f(a, y)) -> F(a, f(f(a, h(f(a, x))), y)) F(x, f(a, y)) -> F(a, x) The TRS R consists of the following rules: f(x, f(a, y)) -> f(a, f(f(a, h(f(a, x))), y)) 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. F(x, f(a, y)) -> F(a, x) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation: POL( F_2(x_1, x_2) ) = x_1 + x_2 + 1 POL( f_2(x_1, x_2) ) = 2x_2 + 1 POL( h_1(x_1) ) = max{0, -2} POL( a ) = 0 popout

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

job log

popout

actions

all output return to TRS Standard