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TRS Stand 20472 pair #381709931
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
n074.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.048467874527 seconds
cpu usage
0.036239469
max memory
3256320.0
stage attributes
key
value
output-size
8571
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 u x y z) (RULES -(s(x),s(y)) -> -(x,y) -(x,0) -> x <=(0,y) -> true <=(s(x),0) -> false <=(s(x),s(y)) -> <=(x,y) f(0,y,0,u) -> true f(0,y,s(z),u) -> false f(s(x),0,z,u) -> f(x,u,-(z,s(x)),u) f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) if(false,x,y) -> y if(true,x,y) -> x perfectp(0) -> false perfectp(s(x)) -> f(x,s(0),s(x),s(x)) ) Problem 1: Innermost Equivalent Processor: -> Rules: -(s(x),s(y)) -> -(x,y) -(x,0) -> x <=(0,y) -> true <=(s(x),0) -> false <=(s(x),s(y)) -> <=(x,y) f(0,y,0,u) -> true f(0,y,s(z),u) -> false f(s(x),0,z,u) -> f(x,u,-(z,s(x)),u) f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) if(false,x,y) -> y if(true,x,y) -> x perfectp(0) -> false perfectp(s(x)) -> f(x,s(0),s(x),s(x)) -> 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(y)) -> -#(x,y) <=#(s(x),s(y)) -> <=#(x,y) F(s(x),0,z,u) -> -#(z,s(x)) F(s(x),0,z,u) -> F(x,u,-(z,s(x)),u) F(s(x),s(y),z,u) -> -#(y,x) F(s(x),s(y),z,u) -> <=#(x,y) F(s(x),s(y),z,u) -> F(s(x),-(y,x),z,u) F(s(x),s(y),z,u) -> F(x,u,z,u) F(s(x),s(y),z,u) -> IF(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) PERFECTP(s(x)) -> F(x,s(0),s(x),s(x)) -> Rules: -(s(x),s(y)) -> -(x,y) -(x,0) -> x <=(0,y) -> true <=(s(x),0) -> false <=(s(x),s(y)) -> <=(x,y) f(0,y,0,u) -> true f(0,y,s(z),u) -> false f(s(x),0,z,u) -> f(x,u,-(z,s(x)),u) f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) if(false,x,y) -> y if(true,x,y) -> x perfectp(0) -> false perfectp(s(x)) -> f(x,s(0),s(x),s(x)) Problem 1: SCC Processor: -> Pairs: -#(s(x),s(y)) -> -#(x,y) <=#(s(x),s(y)) -> <=#(x,y) F(s(x),0,z,u) -> -#(z,s(x)) F(s(x),0,z,u) -> F(x,u,-(z,s(x)),u) F(s(x),s(y),z,u) -> -#(y,x) F(s(x),s(y),z,u) -> <=#(x,y) F(s(x),s(y),z,u) -> F(s(x),-(y,x),z,u) F(s(x),s(y),z,u) -> F(x,u,z,u) F(s(x),s(y),z,u) -> IF(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u)) PERFECTP(s(x)) -> F(x,s(0),s(x),s(x)) -> Rules: -(s(x),s(y)) -> -(x,y) -(x,0) -> x <=(0,y) -> true <=(s(x),0) -> false <=(s(x),s(y)) -> <=(x,y) f(0,y,0,u) -> true f(0,y,s(z),u) -> false f(s(x),0,z,u) -> f(x,u,-(z,s(x)),u) f(s(x),s(y),z,u) -> if(<=(x,y),f(s(x),-(y,x),z,u),f(x,u,z,u))
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