details

property	value
status	complete
benchmark	AC47.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n029.star.cs.uiowa.edu
space	Mixed_AC_and_C

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	3.61653590202 seconds
cpu usage	10.244527449
max memory	7.71919872E8

stage attributes

key	value
output-size	30496
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) EDP (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (7) EDP (8) EUsableRulesReductionPairsProof [EQUIVALENT, 9 ms] (9) EDP (10) PisEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) EDP (13) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (14) EDP (15) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (16) EDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES (19) EDP (20) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (21) EDP (22) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (23) EDP (24) PisEmptyProof [EQUIVALENT, 0 ms] (25) YES (26) EDP (27) ESharpUsableEquationsProof [EQUIVALENT, 0 ms] (28) EDP (29) EDPPoloProof [EQUIVALENT, 0 ms] (30) EDP (31) EDependencyGraphProof [EQUIVALENT, 0 ms] (32) EDP (33) EDPPoloProof [EQUIVALENT, 0 ms] (34) EDP (35) EDependencyGraphProof [EQUIVALENT, 0 ms] (36) TRUE ---------------------------------------- (0) Obligation: Equational 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_1(false, x, y, edge(u, v, i), h) -> reach(x, y, i, edge(u, v, 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)) The set E consists of the following equations: eq(x, y) == eq(y, x) or(x, y) == or(y, x) or(or(x, y), z) == or(x, or(y, z)) ---------------------------------------- (1) EquationalDependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem: The TRS P consists of the following rules: EQ(s(x), s(y)) -> EQ(x, y) UNION(edge(x, y, i), h) -> UNION(i, h) REACH(x, y, edge(u, v, i), h) -> IF_REACH_1(eq(x, u), x, y, edge(u, v, i), h) REACH(x, y, edge(u, v, i), h) -> EQ(x, u) 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_1(true, x, y, edge(u, v, i), h) -> EQ(y, v) IF_REACH_1(false, x, y, edge(u, v, i), h) -> REACH(x, y, i, edge(u, v, h)) 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_2(false, x, y, edge(u, v, i), h) -> REACH(x, y, i, h) IF_REACH_2(false, x, y, edge(u, v, i), h) -> REACH(v, y, union(i, h), empty) IF_REACH_2(false, x, y, edge(u, v, i), h) -> UNION(i, h) OR(or(true, y), ext) -> OR(true, ext) popout

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

job log

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actions

all output return to TRS Equational