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TRS Standard pair #516967170
details
property
value
status
complete
benchmark
#3.13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.77995181084 seconds
cpu usage
7.630664326
max memory
5.25000704E8
stage attributes
key
value
output-size
23164
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 15 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) QDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) QDP (24) QReductionProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPOrderProof [EQUIVALENT, 44 ms] (27) QDP (28) DependencyGraphProof [EQUIVALENT, 0 ms] (29) QDP (30) UsableRulesProof [EQUIVALENT, 0 ms] (31) QDP (32) QReductionProof [EQUIVALENT, 0 ms] (33) QDP (34) QDPSizeChangeProof [EQUIVALENT, 0 ms] (35) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) or(true, y) -> true or(false, y) -> y union(empty, h) -> h union(edge(x, y, i), h) -> edge(x, y, union(i, h)) reach(x, y, empty, h) -> false reach(x, y, edge(u, v, i), h) -> if_reach_1(eq(x, u), x, y, edge(u, v, i), h) if_reach_1(true, x, y, edge(u, v, i), h) -> if_reach_2(eq(y, v), x, y, edge(u, v, i), h) if_reach_2(true, x, y, edge(u, v, i), h) -> true if_reach_2(false, x, y, edge(u, v, i), h) -> or(reach(x, y, i, h), reach(v, y, union(i, h), empty)) if_reach_1(false, x, y, edge(u, v, i), h) -> reach(x, y, i, edge(u, v, h)) 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: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) or(true, y) -> true or(false, y) -> y union(empty, h) -> h union(edge(x, y, i), h) -> edge(x, y, union(i, h)) reach(x, y, empty, h) -> false reach(x, y, edge(u, v, i), h) -> if_reach_1(eq(x, u), x, y, edge(u, v, i), h) if_reach_1(true, x, y, edge(u, v, i), h) -> if_reach_2(eq(y, v), x, y, edge(u, v, i), h) if_reach_2(true, x, y, edge(u, v, i), h) -> true if_reach_2(false, x, y, edge(u, v, i), h) -> or(reach(x, y, i, h), reach(v, y, union(i, h), empty)) if_reach_1(false, x, y, edge(u, v, i), h) -> reach(x, y, i, edge(u, v, h))
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