/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES ** BEGIN proof argument ** All the DP problems were proved finite. As all the involved DP processors are sound, the TRS under analysis terminates. ** END proof argument ** ** BEGIN proof description ** ## Searching for a generalized rewrite rule (a rule whose right-hand side contains a variable that does not occur in the left-hand side)... No generalized rewrite rule found! ## Applying the DP framework... ## 1 initial DP problem to solve. ## First, we try to decompose this problem into smaller problems. ## Round 1 [1 DP problem]: ## DP problem: Dependency pairs = [f^#(f(_0,_1),_2) -> f^#(_0,f(_1,_2)), f^#(f(_0,_1),_2) -> f^#(_1,_2), f^#(g(_0,_1),_2) -> f^#(_0,_2), f^#(g(_0,_1),_2) -> f^#(_1,_2)] TRS = {f(0,_0) -> _0, f(_0,0) -> _0, f(i(_0),_1) -> i(_0), f(f(_0,_1),_2) -> f(_0,f(_1,_2)), f(g(_0,_1),_2) -> g(f(_0,_2),f(_1,_2)), f(1,g(_0,_1)) -> _0, f(2,g(_0,_1)) -> _1} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... Successfully decomposed the DP problem into 1 smaller problem to solve! ## Round 2 [1 DP problem]: ## DP problem: Dependency pairs = [f^#(f(_0,_1),_2) -> f^#(_0,f(_1,_2)), f^#(f(_0,_1),_2) -> f^#(_1,_2)] TRS = {f(0,_0) -> _0, f(_0,0) -> _0, f(i(_0),_1) -> i(_0), f(f(_0,_1),_2) -> f(_0,f(_1,_2)), f(g(_0,_1),_2) -> g(f(_0,_2),f(_1,_2)), f(1,g(_0,_1)) -> _0, f(2,g(_0,_1)) -> _1} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... The constraints are satisfied by the polynomials: {0:[0], g(_0,_1):[1 + _0 + _1], 1:[0], 2:[0], i(_0):[_0], f(_0,_1):[1 + 2 * _0 + _1 + _0 * _1], f^#(_0,_1):[_0]} for all instantiations of the variables with values greater than or equal to mu = 0. This DP problem is finite. ## All the DP problems were proved finite. As all the involved DP processors are sound, the TRS under analysis terminates. Proof run on Linux version 3.10.0-1160.25.1.el7.x86_64 for amd64 using Java version 1.8.0_292 ** END proof description ** Total number of generated unfolded rules = 0