details

property	value
status	complete
benchmark	cime2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	19.9591701031 seconds
cpu usage	59.665629484
max memory	1.933766656E9

stage attributes

key	value
output-size	7652
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 16 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t)) circ(cons(lift, s), cons(a, t)) -> cons(a, circ(s, t)) circ(cons(lift, s), cons(lift, t)) -> cons(lift, circ(s, t)) circ(circ(s, t), u) -> circ(s, circ(t, u)) circ(s, id) -> s circ(id, s) -> s circ(cons(lift, s), circ(cons(lift, t), u)) -> circ(cons(lift, circ(s, t)), u) subst(a, id) -> a msubst(a, id) -> a msubst(msubst(a, s), t) -> msubst(a, circ(s, t)) 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: CIRC(cons(a, s), t) -> MSUBST(a, t) CIRC(cons(a, s), t) -> CIRC(s, t) CIRC(cons(lift, s), cons(a, t)) -> CIRC(s, t) CIRC(cons(lift, s), cons(lift, t)) -> CIRC(s, t) CIRC(circ(s, t), u) -> CIRC(s, circ(t, u)) CIRC(circ(s, t), u) -> CIRC(t, u) CIRC(cons(lift, s), circ(cons(lift, t), u)) -> CIRC(cons(lift, circ(s, t)), u) CIRC(cons(lift, s), circ(cons(lift, t), u)) -> CIRC(s, t) MSUBST(msubst(a, s), t) -> MSUBST(a, circ(s, t)) MSUBST(msubst(a, s), t) -> CIRC(s, t) The TRS R consists of the following rules: circ(cons(a, s), t) -> cons(msubst(a, t), circ(s, t)) circ(cons(lift, s), cons(a, t)) -> cons(a, circ(s, t)) circ(cons(lift, s), cons(lift, t)) -> cons(lift, circ(s, t)) circ(circ(s, t), u) -> circ(s, circ(t, u)) circ(s, id) -> s circ(id, s) -> s circ(cons(lift, s), circ(cons(lift, t), u)) -> circ(cons(lift, circ(s, t)), u) subst(a, id) -> a msubst(a, id) -> a msubst(msubst(a, s), t) -> msubst(a, circ(s, t)) 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. CIRC(cons(a, s), t) -> MSUBST(a, t) CIRC(cons(a, s), t) -> CIRC(s, t) CIRC(cons(lift, s), cons(a, t)) -> CIRC(s, t) CIRC(cons(lift, s), cons(lift, t)) -> CIRC(s, t) CIRC(cons(lift, s), circ(cons(lift, t), u)) -> CIRC(cons(lift, circ(s, t)), u) CIRC(cons(lift, s), circ(cons(lift, t), u)) -> CIRC(s, t) The remaining pairs can at least be oriented weakly. popout

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

job log

popout

actions

all output return to TRS Standard