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TRS Equational pair #487523284
details
property
value
status
complete
benchmark
AC47.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Mixed_AC_and_C
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.630609035492 seconds
cpu usage
0.523386276
max memory
5832704.0
stage attributes
key
value
output-size
22833
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 h i u v x y) (THEORY (AC or) (C eq)) (RULES eq(0,0) -> true eq(0,s(x)) -> false eq(s(x),0) -> false eq(s(x),s(y)) -> eq(x,y) if_reach_1(false,x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h)) if_reach_1(true,x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h) if_reach_2(false,x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty)) if_reach_2(true,x,y,edge(u,v,i),h) -> true or(false,y) -> y or(true,y) -> true reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h) reach(x,y,empty,h) -> false union(edge(x,y,i),h) -> edge(x,y,union(i,h)) union(empty,h) -> h ) Problem 1: Dependency Pairs Processor: -> FAxioms: EQ(x6,x7) = EQ(x7,x6) OR(or(x6,x7),x8) = OR(x6,or(x7,x8)) OR(x6,x7) = OR(x7,x6) -> Pairs: EQ(s(x),s(y)) -> EQ(x,y) IF_REACH_1(false,x,y,edge(u,v,i),h) -> REACH(x,y,i,edge(u,v,h)) IF_REACH_1(true,x,y,edge(u,v,i),h) -> EQ(y,v) IF_REACH_1(true,x,y,edge(u,v,i),h) -> IF_REACH_2(eq(y,v),x,y,edge(u,v,i),h) IF_REACH_2(false,x,y,edge(u,v,i),h) -> OR(reach(x,y,i,h),reach(v,y,union(i,h),empty)) IF_REACH_2(false,x,y,edge(u,v,i),h) -> REACH(v,y,union(i,h),empty) IF_REACH_2(false,x,y,edge(u,v,i),h) -> REACH(x,y,i,h) IF_REACH_2(false,x,y,edge(u,v,i),h) -> UNION(i,h) OR(or(false,y),x6) -> OR(y,x6) OR(or(true,y),x6) -> OR(true,x6) REACH(x,y,edge(u,v,i),h) -> EQ(x,u) REACH(x,y,edge(u,v,i),h) -> IF_REACH_1(eq(x,u),x,y,edge(u,v,i),h) UNION(edge(x,y,i),h) -> UNION(i,h) -> EAxioms: eq(x6,x7) = eq(x7,x6) or(or(x6,x7),x8) = or(x6,or(x7,x8)) or(x6,x7) = or(x7,x6) -> Rules: eq(0,0) -> true eq(0,s(x)) -> false eq(s(x),0) -> false eq(s(x),s(y)) -> eq(x,y) if_reach_1(false,x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h)) if_reach_1(true,x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h) if_reach_2(false,x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty)) if_reach_2(true,x,y,edge(u,v,i),h) -> true or(false,y) -> y or(true,y) -> true reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h) reach(x,y,empty,h) -> false union(edge(x,y,i),h) -> edge(x,y,union(i,h)) union(empty,h) -> h -> SRules: OR(or(x6,x7),x8) -> OR(x6,x7) OR(x6,or(x7,x8)) -> OR(x7,x8) Problem 1: SCC Processor: -> FAxioms: EQ(x6,x7) = EQ(x7,x6) OR(or(x6,x7),x8) = OR(x6,or(x7,x8)) OR(x6,x7) = OR(x7,x6) -> Pairs: EQ(s(x),s(y)) -> EQ(x,y) IF_REACH_1(false,x,y,edge(u,v,i),h) -> REACH(x,y,i,edge(u,v,h)) IF_REACH_1(true,x,y,edge(u,v,i),h) -> EQ(y,v) IF_REACH_1(true,x,y,edge(u,v,i),h) -> IF_REACH_2(eq(y,v),x,y,edge(u,v,i),h) IF_REACH_2(false,x,y,edge(u,v,i),h) -> OR(reach(x,y,i,h),reach(v,y,union(i,h),empty)) IF_REACH_2(false,x,y,edge(u,v,i),h) -> REACH(v,y,union(i,h),empty) IF_REACH_2(false,x,y,edge(u,v,i),h) -> REACH(x,y,i,h) IF_REACH_2(false,x,y,edge(u,v,i),h) -> UNION(i,h) OR(or(false,y),x6) -> OR(y,x6) OR(or(true,y),x6) -> OR(true,x6) REACH(x,y,edge(u,v,i),h) -> EQ(x,u) REACH(x,y,edge(u,v,i),h) -> IF_REACH_1(eq(x,u),x,y,edge(u,v,i),h) UNION(edge(x,y,i),h) -> UNION(i,h) -> EAxioms: eq(x6,x7) = eq(x7,x6) or(or(x6,x7),x8) = or(x6,or(x7,x8)) or(x6,x7) = or(x7,x6)
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