details

property	value
status	complete
benchmark	size-12-alpha-3-num-123.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n178.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	7.51708602905 seconds
cpu usage	26.736625311
max memory	1.476886528E9

stage attributes

key	value
output-size	5409
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 2 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 33 ms] (4) QDP (5) QDPOrderProof [EQUIVALENT, 106 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 39 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(x1) -> x1 a(a(b(x1))) -> c(b(a(a(x1)))) b(c(x1)) -> a(b(x1)) 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: A(a(b(x1))) -> B(a(a(x1))) A(a(b(x1))) -> A(a(x1)) A(a(b(x1))) -> A(x1) B(c(x1)) -> A(b(x1)) B(c(x1)) -> B(x1) The TRS R consists of the following rules: a(x1) -> x1 a(a(b(x1))) -> c(b(a(a(x1)))) b(c(x1)) -> a(b(x1)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. A(a(b(x1))) -> A(a(x1)) A(a(b(x1))) -> A(x1) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(A(x_1)) = x_1 POL(B(x_1)) = 1 + x_1 POL(a(x_1)) = x_1 POL(b(x_1)) = 1 + x_1 POL(c(x_1)) = x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: a(x1) -> x1 a(a(b(x1))) -> c(b(a(a(x1)))) b(c(x1)) -> a(b(x1)) ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: A(a(b(x1))) -> B(a(a(x1))) B(c(x1)) -> A(b(x1)) B(c(x1)) -> B(x1) popout

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

job log

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actions

all output return to SRS Standard