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TRS Standard pair #516968136
details
property
value
status
complete
benchmark
t003.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.108078956604 seconds
cpu usage
0.045576562
max memory
3280896.0
stage attributes
key
value
output-size
10962
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 u:S x:S y:S z:S) (RULES -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S <=(0,y:S) -> ttrue <=(s(x:S),0) -> ffalse <=(s(x:S),s(y:S)) -> <=(x:S,y:S) f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,-(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S <=(0,y:S) -> ttrue <=(s(x:S),0) -> ffalse <=(s(x:S),s(y:S)) -> <=(x:S,y:S) f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,-(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) <=#(s(x:S),s(y:S)) -> <=#(x:S,y:S) F(s(x:S),0,z:S,u:S) -> -#(z:S,s(x:S)) F(s(x:S),0,z:S,u:S) -> F(x:S,u:S,-(z:S,s(x:S)),u:S) F(s(x:S),s(y:S),z:S,u:S) -> -#(y:S,x:S) F(s(x:S),s(y:S),z:S,u:S) -> <=#(x:S,y:S) F(s(x:S),s(y:S),z:S,u:S) -> F(s(x:S),-(y:S,x:S),z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> IF(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) PERFECTP(s(x:S)) -> F(x:S,s(0),s(x:S),s(x:S)) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S <=(0,y:S) -> ttrue <=(s(x:S),0) -> ffalse <=(s(x:S),s(y:S)) -> <=(x:S,y:S) f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,-(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) Problem 1: SCC Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) <=#(s(x:S),s(y:S)) -> <=#(x:S,y:S) F(s(x:S),0,z:S,u:S) -> -#(z:S,s(x:S)) F(s(x:S),0,z:S,u:S) -> F(x:S,u:S,-(z:S,s(x:S)),u:S) F(s(x:S),s(y:S),z:S,u:S) -> -#(y:S,x:S) F(s(x:S),s(y:S),z:S,u:S) -> <=#(x:S,y:S) F(s(x:S),s(y:S),z:S,u:S) -> F(s(x:S),-(y:S,x:S),z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> IF(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) PERFECTP(s(x:S)) -> F(x:S,s(0),s(x:S),s(x:S)) -> Rules: -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S <=(0,y:S) -> ttrue <=(s(x:S),0) -> ffalse <=(s(x:S),s(y:S)) -> <=(x:S,y:S) f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,-(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(<=(x:S,y:S),f(s(x:S),-(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S))
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