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TRS_Equational 2019-03-21 05.09 pair #429997210
details
property
value
status
complete
benchmark
AC51.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.78257 seconds
cpu usage
3.80615
user time
3.65855
system time
0.147601
max virtual memory
1.8343352E7
max residence set size
235488.0
stage attributes
key
value
starexec-result
YES
output
3.58/1.75 YES 3.58/1.75 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 3.58/1.75 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.58/1.75 3.58/1.75 3.58/1.75 Termination of the given ETRS could be proven: 3.58/1.75 3.58/1.75 (0) ETRS 3.58/1.75 (1) RRRPoloETRSProof [EQUIVALENT, 138 ms] 3.58/1.75 (2) ETRS 3.58/1.75 (3) RRRPoloETRSProof [EQUIVALENT, 0 ms] 3.58/1.75 (4) ETRS 3.58/1.75 (5) RisEmptyProof [EQUIVALENT, 0 ms] 3.58/1.75 (6) YES 3.58/1.75 3.58/1.75 3.58/1.75 ---------------------------------------- 3.58/1.75 3.58/1.75 (0) 3.58/1.75 Obligation: 3.58/1.75 Equational rewrite system: 3.58/1.75 The TRS R consists of the following rules: 3.58/1.75 3.58/1.75 plus(0, y) -> y 3.58/1.75 plus(s(x), 0) -> s(x) 3.58/1.75 plus(s(x), s(y)) -> s(plus(s(x), plus(y, 0))) 3.58/1.75 3.58/1.75 The set E consists of the following equations: 3.58/1.75 3.58/1.75 plus(x, y) == plus(y, x) 3.58/1.75 plus(plus(x, y), z) == plus(x, plus(y, z)) 3.58/1.75 3.58/1.75 3.58/1.75 ---------------------------------------- 3.58/1.75 3.58/1.75 (1) RRRPoloETRSProof (EQUIVALENT) 3.58/1.75 The following E TRS is given: Equational rewrite system: 3.58/1.75 The TRS R consists of the following rules: 3.58/1.75 3.58/1.75 plus(0, y) -> y 3.58/1.75 plus(s(x), 0) -> s(x) 3.58/1.75 plus(s(x), s(y)) -> s(plus(s(x), plus(y, 0))) 3.58/1.75 3.58/1.75 The set E consists of the following equations: 3.58/1.76 3.58/1.76 plus(x, y) == plus(y, x) 3.58/1.76 plus(plus(x, y), z) == plus(x, plus(y, z)) 3.58/1.76 3.58/1.76 The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: 3.58/1.76 3.58/1.76 plus(s(x), s(y)) -> s(plus(s(x), plus(y, 0))) 3.58/1.76 Used ordering: 3.58/1.76 Polynomial interpretation [POLO]: 3.58/1.76 3.58/1.76 POL(0) = 0 3.58/1.76 POL(plus(x_1, x_2)) = x_1 + x_1*x_2 + x_2 3.58/1.76 POL(s(x_1)) = 1 + x_1 3.58/1.76 3.58/1.76 3.58/1.76 3.58/1.76 3.58/1.76 ---------------------------------------- 3.58/1.76 3.58/1.76 (2) 3.58/1.76 Obligation: 3.58/1.76 Equational rewrite system: 3.58/1.76 The TRS R consists of the following rules: 3.58/1.76 3.58/1.76 plus(0, y) -> y 3.58/1.76 plus(s(x), 0) -> s(x) 3.58/1.76 3.58/1.76 The set E consists of the following equations: 3.58/1.76 3.58/1.76 plus(x, y) == plus(y, x) 3.58/1.76 plus(plus(x, y), z) == plus(x, plus(y, z)) 3.58/1.76 3.58/1.76 3.58/1.76 ---------------------------------------- 3.58/1.76 3.58/1.76 (3) RRRPoloETRSProof (EQUIVALENT) 3.58/1.76 The following E TRS is given: Equational rewrite system: 3.58/1.76 The TRS R consists of the following rules: 3.58/1.76 3.58/1.76 plus(0, y) -> y 3.58/1.76 plus(s(x), 0) -> s(x) 3.58/1.76 3.58/1.76 The set E consists of the following equations: 3.58/1.76 3.58/1.76 plus(x, y) == plus(y, x) 3.58/1.76 plus(plus(x, y), z) == plus(x, plus(y, z)) 3.58/1.76 3.58/1.76 The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering: 3.58/1.76 3.58/1.76 plus(0, y) -> y 3.58/1.76 plus(s(x), 0) -> s(x) 3.58/1.76 Used ordering: 3.58/1.76 Polynomial interpretation [POLO]: 3.58/1.76 3.58/1.76 POL(0) = 0 3.58/1.76 POL(plus(x_1, x_2)) = 1 + x_1 + x_2
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