details

property	value
status	complete
benchmark	#3.21.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n103.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.76232194901 seconds
cpu usage	3.835733242
max memory	1.94134016E8

stage attributes

key	value
output-size	4929
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) MRRProof [EQUIVALENT, 0 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: times(x, plus(y, 1)) -> plus(times(x, plus(y, times(1, 0))), x) times(x, 1) -> x plus(x, 0) -> x times(x, 0) -> 0 Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: times(x, plus(y, 1)) -> plus(times(x, plus(y, times(1, 0))), x) times(x, 1) -> x plus(x, 0) -> x times(x, 0) -> 0 The set Q consists of the following terms: times(x0, plus(x1, 1)) times(x0, 1) plus(x0, 0) times(x0, 0) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: TIMES(x, plus(y, 1)) -> PLUS(times(x, plus(y, times(1, 0))), x) TIMES(x, plus(y, 1)) -> TIMES(x, plus(y, times(1, 0))) TIMES(x, plus(y, 1)) -> PLUS(y, times(1, 0)) TIMES(x, plus(y, 1)) -> TIMES(1, 0) The TRS R consists of the following rules: times(x, plus(y, 1)) -> plus(times(x, plus(y, times(1, 0))), x) times(x, 1) -> x plus(x, 0) -> x times(x, 0) -> 0 The set Q consists of the following terms: times(x0, plus(x1, 1)) times(x0, 1) plus(x0, 0) times(x0, 0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) DependencyGraphProof (EQUIVALENT) popout

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