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	n139.star.cs.uiowa.edu
space	Mixed_AC_and_C

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.87421 seconds
cpu usage	7.12611
user time	6.871
system time	0.255115
max virtual memory	1.827784E7
max residence set size	538400.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ETRS could be proven: (0) ETRS (1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms] (2) EDP (3) EDependencyGraphProof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, 0 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) 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) popout

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

job log

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actions

all output return to TRS Equational