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TRS Innermost pair #487524656
details
property
value
status
complete
benchmark
wiehe13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Mixed_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.492557048798 seconds
cpu usage
0.424346604
max memory
8667136.0
stage attributes
key
value
output-size
16380
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES gt(s(x:S),s(y:S)) -> gt(x:S,y:S) gt(s(x:S),zero) -> ttrue gt(zero,y:S) -> ffalse id(x:S) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S not(x:S) -> if(x:S,ffalse,ttrue) plus(id(x:S),s(y:S)) -> s(plus(x:S,if(gt(s(y:S),y:S),y:S,s(y:S)))) plus(s(x:S),s(y:S)) -> s(s(plus(if(gt(x:S,y:S),x:S,y:S),if(not(gt(x:S,y:S)),id(x:S),id(y:S))))) plus(s(x:S),x:S) -> plus(if(gt(x:S,x:S),id(x:S),id(x:S)),s(x:S)) plus(zero,y:S) -> y:S quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: GT(s(x:S),s(y:S)) -> GT(x:S,y:S) NOT(x:S) -> IF(x:S,ffalse,ttrue) PLUS(s(x:S),s(y:S)) -> GT(x:S,y:S) PLUS(s(x:S),s(y:S)) -> ID(x:S) PLUS(s(x:S),s(y:S)) -> ID(y:S) PLUS(s(x:S),s(y:S)) -> IF(gt(x:S,y:S),x:S,y:S) PLUS(s(x:S),s(y:S)) -> IF(not(gt(x:S,y:S)),id(x:S),id(y:S)) PLUS(s(x:S),s(y:S)) -> NOT(gt(x:S,y:S)) PLUS(s(x:S),s(y:S)) -> PLUS(if(gt(x:S,y:S),x:S,y:S),if(not(gt(x:S,y:S)),id(x:S),id(y:S))) PLUS(s(x:S),x:S) -> GT(x:S,x:S) PLUS(s(x:S),x:S) -> ID(x:S) PLUS(s(x:S),x:S) -> IF(gt(x:S,x:S),id(x:S),id(x:S)) PLUS(s(x:S),x:S) -> PLUS(if(gt(x:S,x:S),id(x:S),id(x:S)),s(x:S)) QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> PLUS(z:S,s(0)) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,plus(z:S,s(0)),s(z:S)) -> Rules: gt(s(x:S),s(y:S)) -> gt(x:S,y:S) gt(s(x:S),zero) -> ttrue gt(zero,y:S) -> ffalse id(x:S) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S not(x:S) -> if(x:S,ffalse,ttrue) plus(id(x:S),s(y:S)) -> s(plus(x:S,if(gt(s(y:S),y:S),y:S,s(y:S)))) plus(s(x:S),s(y:S)) -> s(s(plus(if(gt(x:S,y:S),x:S,y:S),if(not(gt(x:S,y:S)),id(x:S),id(y:S))))) plus(s(x:S),x:S) -> plus(if(gt(x:S,x:S),id(x:S),id(x:S)),s(x:S)) plus(zero,y:S) -> y:S quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) Problem 1: SCC Processor: -> Pairs: GT(s(x:S),s(y:S)) -> GT(x:S,y:S) NOT(x:S) -> IF(x:S,ffalse,ttrue) PLUS(s(x:S),s(y:S)) -> GT(x:S,y:S) PLUS(s(x:S),s(y:S)) -> ID(x:S) PLUS(s(x:S),s(y:S)) -> ID(y:S) PLUS(s(x:S),s(y:S)) -> IF(gt(x:S,y:S),x:S,y:S) PLUS(s(x:S),s(y:S)) -> IF(not(gt(x:S,y:S)),id(x:S),id(y:S)) PLUS(s(x:S),s(y:S)) -> NOT(gt(x:S,y:S)) PLUS(s(x:S),s(y:S)) -> PLUS(if(gt(x:S,y:S),x:S,y:S),if(not(gt(x:S,y:S)),id(x:S),id(y:S))) PLUS(s(x:S),x:S) -> GT(x:S,x:S) PLUS(s(x:S),x:S) -> ID(x:S) PLUS(s(x:S),x:S) -> IF(gt(x:S,x:S),id(x:S),id(x:S)) PLUS(s(x:S),x:S) -> PLUS(if(gt(x:S,x:S),id(x:S),id(x:S)),s(x:S)) QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> PLUS(z:S,s(0)) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,plus(z:S,s(0)),s(z:S)) -> Rules: gt(s(x:S),s(y:S)) -> gt(x:S,y:S) gt(s(x:S),zero) -> ttrue gt(zero,y:S) -> ffalse id(x:S) -> x:S if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S not(x:S) -> if(x:S,ffalse,ttrue) plus(id(x:S),s(y:S)) -> s(plus(x:S,if(gt(s(y:S),y:S),y:S,s(y:S)))) plus(s(x:S),s(y:S)) -> s(s(plus(if(gt(x:S,y:S),x:S,y:S),if(not(gt(x:S,y:S)),id(x:S),id(y:S))))) plus(s(x:S),x:S) -> plus(if(gt(x:S,x:S),id(x:S),id(x:S)),s(x:S)) plus(zero,y:S) -> y:S quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S)))
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