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	n072.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	19.143 seconds
cpu usage	49.7056
user time	47.4653
system time	2.2403
max virtual memory	1.860848E7
max residence set size	4776888.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 6 ms] (2) QDP (3) QDPOrderProof [EQUIVALENT, 18 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. Used ordering: Polynomial interpretation [POLO]: POL(CIRC(x_1, x_2)) = x_1 + x_1*x_2 POL(MSUBST(x_1, x_2)) = x_1 + x_1*x_2 POL(circ(x_1, x_2)) = x_1 + x_1*x_2 + x_2 POL(cons(x_1, x_2)) = 1 + x_1 + x_2 popout

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

job log

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actions

all output return to TRS Standard