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TRS Equational pair #487523131
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
n141.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.694608211517 seconds
cpu usage
0.598921417
max memory
4624384.0
stage attributes
key
value
output-size
16692
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x y) (THEORY (AC plus)) (RULES plus(0,y) -> y plus(s(x),0) -> s(x) plus(s(x),s(y)) -> s(plus(s(x),plus(y,0))) ) Problem 1: Dependency Pairs Processor: -> FAxioms: PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4)) PLUS(x2,x3) = PLUS(x3,x2) -> Pairs: PLUS(plus(0,y),x2) -> PLUS(y,x2) PLUS(plus(s(x),0),x2) -> PLUS(s(x),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(plus(s(x),plus(y,0))),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(x),plus(y,0)) PLUS(plus(s(x),s(y)),x2) -> PLUS(y,0) PLUS(s(x),s(y)) -> PLUS(s(x),plus(y,0)) PLUS(s(x),s(y)) -> PLUS(y,0) -> EAxioms: plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4)) plus(x2,x3) = plus(x3,x2) -> Rules: plus(0,y) -> y plus(s(x),0) -> s(x) plus(s(x),s(y)) -> s(plus(s(x),plus(y,0))) -> SRules: PLUS(plus(x2,x3),x4) -> PLUS(x2,x3) PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4) Problem 1: SCC Processor: -> FAxioms: PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4)) PLUS(x2,x3) = PLUS(x3,x2) -> Pairs: PLUS(plus(0,y),x2) -> PLUS(y,x2) PLUS(plus(s(x),0),x2) -> PLUS(s(x),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(plus(s(x),plus(y,0))),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(x),plus(y,0)) PLUS(plus(s(x),s(y)),x2) -> PLUS(y,0) PLUS(s(x),s(y)) -> PLUS(s(x),plus(y,0)) PLUS(s(x),s(y)) -> PLUS(y,0) -> EAxioms: plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4)) plus(x2,x3) = plus(x3,x2) -> Rules: plus(0,y) -> y plus(s(x),0) -> s(x) plus(s(x),s(y)) -> s(plus(s(x),plus(y,0))) -> SRules: PLUS(plus(x2,x3),x4) -> PLUS(x2,x3) PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(plus(0,y),x2) -> PLUS(y,x2) PLUS(plus(s(x),0),x2) -> PLUS(s(x),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(plus(s(x),plus(y,0))),x2) PLUS(plus(s(x),s(y)),x2) -> PLUS(s(x),plus(y,0)) PLUS(plus(s(x),s(y)),x2) -> PLUS(y,0) PLUS(s(x),s(y)) -> PLUS(s(x),plus(y,0)) PLUS(s(x),s(y)) -> PLUS(y,0) -> FAxioms: plus(plus(x2,x3),x4) -> plus(x2,plus(x3,x4)) plus(x2,x3) -> plus(x3,x2) PLUS(plus(x2,x3),x4) -> PLUS(x2,plus(x3,x4)) PLUS(x2,x3) -> PLUS(x3,x2) -> EAxioms: plus(plus(x2,x3),x4) = plus(x2,plus(x3,x4)) plus(x2,x3) = plus(x3,x2) ->->-> Rules: plus(0,y) -> y plus(s(x),0) -> s(x) plus(s(x),s(y)) -> s(plus(s(x),plus(y,0))) -> SRules: PLUS(plus(x2,x3),x4) -> PLUS(x2,x3) PLUS(x2,plus(x3,x4)) -> PLUS(x3,x4) Problem 1: Reduction Pairs Processor: -> FAxioms: PLUS(plus(x2,x3),x4) = PLUS(x2,plus(x3,x4)) PLUS(x2,x3) = PLUS(x3,x2)
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